University General Course Catalog 2018-2019 
    
    Apr 24, 2024  
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8. Course Descriptions

Note: Sequencing rules in effect for many Math courses prohibit students from earning credit for a lower numbered Math course after receiving credit for a higher numbered Math course. Sequencing rules are included in the course descriptions of applicable courses.
 

Mathematics
  

  • MATH 19 - Fundamentals of College Mathematics I

    (3 units)
    The first half of a 2-semester course covering MATH 120  content. Presentation is adapted to needs of students with learning or physical disabilities. Enrollment by departmental permission. (Credit does not apply to any baccalaureate degree program.)

    Prerequisite(s): ACT score of 21 or SAT score of 500 or revised SAT score of 530 or MATH 096 with a “C” or above or an “S”.

    Grading Basis: S/U only
    Units of Lecture: 3
    Offered: Every Fall

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. formulate and use mathematical models to analyze real-world situations.
    2. determine and implement an appropriate method of solution for financial problems.
    3. solve basic probability problems.


    Click here for course scheduling information. | Check course textbook information
  

  • MATH 95 - Elementary Algebra

    (0 units)
    Preparation for Intermediate Algebra. Topics include the fundamental operations on real numbers, inequalities in one variable, polynomials, integer exponents, and solving quadratic equations by factoring. Credits do not apply toward any baccalaureate program. (Departmental consent is required to drop this course.)

    Grading Basis: S/U only
    Offered: Every Fall, Spring, and Summer

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. identify, simplify and calculate using laws of exponents, order of operations.
    2. compute fluently with fractions, decimals, percents, and integers.
    3. simplify and evaluating algebraic expressions.
    4. solve linear equations and inequalities.
    5. identify the components of the Cartesian coordinate system.
    6. create and interpret graphs.
    7. solve systems of linear equations.


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  • MATH 96 - Intermediate Algebra

    (0 units)
    Basic properties of the real numbers; standard algebraic techniques, including exponents, factoring, fractions, radicals; problem solving; linear and quadratic equations; the concept of graphing. (Credit does not apply to any baccalaureate degree program.) (Departmental consent is required to drop this course.)

    Prerequisite(s): ACT math score of 19 or SAT math score of 470 or revised SAT math score of 510 or satisfactory score on an appropriate placement test as determined by the Math & Stat Department or MATH 95 .

    Grading Basis: S/U only
    Offered: Every Fall, Spring, and Summer

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. simplify, add, subtract, multiply, and divide rational expressions and functions.
    2. simplify, add, subtract, multiply, and divide radical expressions and functions.
    3. solve quadratic equations by factoring, using the square root property, completing the square, and by the quadratic formula.
    4. solve compound inequalities, absolute value inequalities, and absolute value equations.
    5. solve and graph linear equations and inequalities in two variables.
    6. recognize function notation and distinguish functions from relations.
    7. simplify expressions with integer and rational exponents.


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  • MATH 96A - Intermediate Algebra - Basic Properties

    (0 units)
    Basic properties of the real numbers; problem solving, linear equations. Graphing functions. (Credit does not apply to any baccalaureate degree program.) (Departmental consent is required to drop this course.)

    Prerequisite(s): ACT math score of 19, or SAT math score of 470, or revised SAT math score of 510, or satisfactory score on an appropriate placement test as determined by the Math & Stat Department, or MATH 95 .

    Grading Basis: S/U only
    Offered: Every Fall, Spring, and Summer

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. demonstrate their understanding of the importance of the correct order of operations by evaluating expressions, either in writing or verbally when called upon in class, as to the application of the correct order of operations.
    2. demonstrate their ability to simplify algebraic expressions when called upon in class, or in writing, or both.
    3. demonstrate their understanding of how to simplify exponential expressions through application of rules of exponents.


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  • MATH 96D - Algebra Review for Math 126

    (0 units)
    Multiplying, dividing and factoring polynomial expressions. Solving polynomial and rational equations. Algebraic techniques involving exponents and radicals. (Credit does not apply toward any baccalaureate degree program.) (Departmental consent is required to drop this course.)

    Prerequisite(s): MATH 96A  or ACT math score of 20 or SAT math score of 480 or revised SAT score of 520 or satisfactory score on an appropriate placement test as determined by the Math & Stat Department.

    Grading Basis: S/U only
    Offered: Every Fall, Spring, and Summer

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. demonstrate their ability to divide and then factor polynomials through in-class presentation, in writing, or both.
    2. demonstrate their ability to add, subtract, multiply or divide rational expressions through either or both of in-class presentations and written assignments.
    3. demonstrate their ability to simplify expressions, either through in-class participation or in writing, or both, using the laws of exponents.


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  • MATH 119 - Fundamentals of College Mathematics II

    (3 units)
    A continuation of MATH 19  covering remaining topics of MATH 120 . Presentation is adapted to needs of students with learning or physical disabilities. Enrollment by departmental permission. (This course satisfies the University Core Mathematics requirement.)

    Prerequisite(s): MATH 19.

    Units of Lecture: 3
    Offered: Every Spring

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. formulate and use mathematical models to analyze real-world situations.
    2. determine and implement an appropriate method of solution for financial problems.
    3. solve basic probability problems.


    Click here for course scheduling information. | Check course textbook information
  

  • MATH 120 - Fundamentals of College Mathematics

    (3 units) CO2
    Sets, logic; probability, statistics; consumer mathematics; variation; geometry and trigonometry for measurement; linear, quadratic, exponential and logarithmic functions. Emphasis on problem solving and applications. (Credit may not be received for MATH 120 if credit has already been awarded for MATH 127 or above. This course satisfies the University Core Mathematics requirement.)

    Prerequisite(s): ACT score of 22 or SAT score of 500 or revised SAT score of 530 or MATH 96  with a “C” or above or an “S”.

    Units of Lecture: 3
    Offered: Every Fall, Spring, and Summer

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. formulate and use mathematical models to analyze real-world situations.
    2. determine and implement an appropriate method of solution for financial problems.
    3. solve basic probability problems.


    Click here for course scheduling information. | Check course textbook information
  

  • MATH 120E - Fundamentals of College Mathematics Expanded

    (3 units) CO2
    Covers the same material as Math 120 and requires concurrent enrollment in a specific section of Math 96A. Students who enroll in Math 120E will be added to the correct section of Math 96A by Admissions & Records staff within 2 working days. This course satisfies the University Core Mathematics requirement.

    Prerequisite(s): ACT Math score of 19 or SAT Math score of 470 or revised SAT score of 510 or Accuplacer EA score of 76 or MATH 95 . Corequisite(s): MATH 96A .

    Units of Lecture: 3
    Offered: Every Fall, Spring, and Summer

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. formulate and use mathematical models to analyze real-world situations.
    2. determine and implement and appropriate method of solution for financial problems.
    3. solve basic probability problems.


    Click here for course scheduling information. | Check course textbook information
  

  • MATH 122 - Number Concepts for Elementary School Teachers

    (3 units)
    Mathematics needed by those teaching new-content mathematics at the elementary school level with emphasis on the structure of the real number system and its subsystems. Open only to elementary, dual, and special education majors and to others with department approval.

    Prerequisite(s): ACT score of 22, SAT score of 500, satisfactory score on a suitable readiness exam, or completion of Core Math.

    Units of Lecture: 3
    Offered: Every Fall and Spring

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. add subtract multiply and divide integers, rational numbers, and real numbers in standard and non-standard ways.
    2. solve, create, and interpret elementary fraction problems.
    3. solve, create, and interpret elementary percent, decimal and ratio problems.


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  • MATH 123 - Statistical and Geometrical Concepts for Elementary School Teachers

    (3 units)
    Continuation of MATH 122 . (This course does not satisfy the university core mathematics requirement.)

    Prerequisite(s): MATH 122 .

    Units of Lecture: 3
    Offered: Every Fall and Spring

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. identify, classify, and discuss basic geometric shapes used in K-8 classrooms.
    2. apply and invent formulas for volume, area, surface area and perimeter on basic geometric shapes and extensions of those shapes.
    3. calculate statistical formulas including mean, mode, median, standard deviation and range on small data sets and interpret their meanings.


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  • MATH 126 - Precalculus I

    (3 units) CO2
    Fundamentals of algebra; polynomial, rational, exponential, and logarithmic functions, their graphs, and applications; complex numbers; absolute value and quadratic inequalities; systems of equations, matrices, determinants. (Credit may not be received for MATH 126 if credit has already been awarded for MATH 128 . This course satisfies the University Core Mathematics requirement).

    Prerequisite(s): ACT score of 22, SAT score of 500 or revised SAT score of 530, or MATH 96  with a “C” or above or an “S”. 
    *Credit may not be received for MATH 126 if credit has already been awarded for MATH 128  or above.

    Units of Lecture: 2
    Units of Discussion/Recitation: 1
    Offered: Every Fall, Spring, and Summer

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. graph rational functions.
    2. solve equations involving exponential or logarithmic functions.
    3. solve inequalities involving rational functions.


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  • MATH 126E - Precalculus I Expanded

    (3 units) CO2
    Covers the same material as MATH 126 and requires concurrent enrollment in a specific section of MATH 96D. Students who enroll in MATH 126E will be added to the correct section of MATH 96D by Admissions & Records staff within 2 working days. May satisfy the Core Mathematics requirement for some majors.

    Prerequisite(s): MATH 96A  or ACT score of 20 or SAT score of 490 or revised SAT 520. Corequisite(s): MATH 96D .

    Units of Lecture: 3
    Offered: Every Fall, Spring, and Summer

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. graph rational functions.
    2. solve equations involving exponential or logarithmic functions.
    3. solve inequalities involving rational functions.


    Click here for course scheduling information. | Check course textbook information
  

  • MATH 127 - Precalculus II

    (3 units) CO2
    Trigonometric functions, identities and equations; conic sections; complex numbers; polar coordinates, vectors; systems of equations, Matrix algebra and more. (Credit may not be received for MATH 127 if credit has already been awarded for MATH 128. This course satisfies the University Core Mathematics requirement).

    Prerequisite(s): ACT score of 27, SAT score of 610 or revised SAT score of 630, or MATH 126  with a “C-” or better.
    * Credit may not be received for both MATH 127 and MATH 128 .

    Units of Lecture: 2
    Units of Discussion/Recitation: 1
    Offered: Every Fall, Spring, and Summer

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. solve trigonometric equations.
    2. convert between Cartesian and polar coordinates.
    3. analyze equations of central conics such as ellipses and hyperbolas.


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  • MATH 128 - Precalculus and Trigonometry

    (5 units) CO2
    Equations, relations, functions, graphing; polynomial, rational, exponential, logarithmic, and circular functions with applications; coordinate geometry of lines and conics; analytic trigonometry; matrices, determinants; binomial theorem. (Credit may not be received for MATH 128 if credit has already been awarded for MATH 181  or above. This course satisfies the University Core Mathematics requirement.)

    Prerequisite(s): ACT score of 27, SAT score of 610, revised SAT score 630, or satisfactory score on an appropriate placement test as determined by the Math/Stat department.

    Units of Lecture: 5
    Offered: Every Fall

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. analyze algebraic functions such as rational, exponentials, and logarithmic functions.
    2. solve trigonometric equations.
    3. convert between Cartesian and polar coordinates.


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  • MATH 176 - Introductory Calculus for Business and Social Sciences

    (3 units) CO2
    Fundamental ideas of analytic geometry and calculus, plane coordinates, graphs, functions, limits, derivatives, integrals, the fundamental theorem of calculus, rates, extrema and applications thereof. (This course satisfies the University Core Mathematics requirement. Credit may not be received for Math 176 if credit has already been awarded for MATH 181  or above.)

    Prerequisite(s): ACT score of 27 or SAT score of 610 or revised SAT score of 630 or MATH 126  with a “C-” or better.

    Units of Lecture: 2
    Units of Discussion/Recitation: 1
    Offered: Every Fall, Spring, and Summer

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. use and apply the concepts and terminology of rate of change through applications and examples.
    2. compute the derivative of a function using rules of differentiation.
    3. compute basic integrals using the Fundamental Theorem of Calculus.


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  • MATH 181 - Calculus I

    (4 units) CO2
    Fundamental concepts of analytic geometry and calculus; functions, graphs, limits, derivatives and integrals. (This course satisfies the University Core Mathematics requirement.)

    Prerequisite(s): MATH 127  or MATH 128  with a “C-” or better or an ACT score of 28 or an SAT score of 630 or a revised SAT score of 650.

    Units of Lecture: 3
    Units of Discussion/Recitation: 1
    Offered: Every Fall, Spring, and Summer

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. demonstrate an understanding of the concepts and terminology of limits through applications and examples.
    2. compute the derivative of a function using the definition, rules of differentiation, slopes of tangent lines, and describe it as a rate of change, in a number of natural and physical phenomena.
    3. compute basic integrals using Riemann sums as well as the Fundamental Theorem of Calculus.


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  • MATH 182 - Calculus II

    (4 units)
    Methods of integration. Sequences and series, power series.

    Prerequisite(s): MATH 181  with a “C-” or better.

    Units of Lecture: 3
    Units of Discussion/Recitation: 1
    Offered: Every Fall, Spring, and Summer

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. evaluate definite and indefinite integrals using various techniques of integration: e.g. substitution, integration by parts and partial fractions.
    2. apply integration to compute arc-lengths, areas, and volumes of revolution.
    3. test infinite series for convergence; represent functions using power series.


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  • MATH 253 - Matrix Algebra

    (3 units)
    Introduces linear algebra, including matrices, determinants, vector spaces, linear transformations, eigenvectors and eigenvalues.

    Prerequisite(s): MATH 182  with a “C-” or better.

    Units of Lecture: 3
    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. represent systems of equations using matrices.
    2. solve matrix equations using Gaussian elimination.
    3. demonstrate an understanding of the fundamental concepts of finite dimensional vector spaces.
    4. find the eigenvalues and eigenvectors of a given square matrix.


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  • MATH 283 - Calculus III

    (4 units)
    Continuation of MATH 182  ; infinite series, three-dimensional calculus.

    Prerequisite(s): MATH 182  with a “C-” or better.

    Units of Lecture: 4
    Offered: Every Fall, Spring, and Summer

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. calculate dot products, crossed products; find partial derivatives of functions of several variables.
    2. solve optimization problems.
    3. setup and evaluate double and triple integrals.
    4. work with vector fields; e.g. compute the curl and divergence.
    5. use integral theorems of multivariable calculus: e.g. Green’s theorem.


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  • MATH 285 - Differential Equations

    (3 units)
    Theory and solving techniques for: constant and variable coefficient linear equations, a variety of non-linear equations. Emphasis on those differential equations arising from real-world phenomena.

    Prerequisite(s): MATH 182  with a “C-” or better. Recommended Preparation: MATH 283  with a “C-” or better.

    Units of Lecture: 3
    Offered: Every Fall, Spring, and Summer

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. use qualitative methods to assess the behavior of solutions without solving an equation.
    2. demonstrate understanding of some of the different techniques for solving first and higher order homogeneous and nonhomogeneous equations: e.g. the integrating factor method, separable variables, the Laplace transform.
    3. solve systems of differential equations with constant coefficients.


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  • MATH 295 - Proof Writing for Math/Stat Major

    (3 units)
    Foundations of mathematical proof writing for advanced courses in the Math/Stat majors. Proof methods will be applied to topics in logic; mathematical induction; elementary set theory; functions; properties of integers and real numbers.

    Prerequisite(s): MATH 283  with a “C” or better.

    Grading Basis: Graded
    Units of Lecture: 3
    Offered: Every Fall, Spring, and Summer

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. write cogent proofs using different methods like direct proof, indirect proof, proof by contradiction, proof by induction.
    2. demonstrate an understanding of basic concepts about operations with sets and functions, including one-to-one and onto functions, direct image and inverse image.
    3. work with equivalence classes and identify the quotient set determined by an equivalence relation.


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  • MATH 301 - Introduction to Proofs: Logic, Sets and Functions

    (3 units)
    Logic; mathematical induction; elementary set theory; functions; properties of integers and real numbers. Heavy stress on mathematical proofs. Credit may not be received for MATH 301 if credit has already been awarded for MATH 310 .

    Prerequisite(s): MATH 283  with a “C” or better.

    Units of Lecture: 3
    Offered: Every Fall, Spring, and Summer

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. write cogent proofs using different methods like direct proof, indirect proof, proof by contradiction, proof by induction.
    2. demonstrate an understanding of basic concepts about operations with sets and functions, including one-to-one and onto functions, direct image and inverse image.
    3. work with equivalence classes and identify the quotient set determined by an equivalence relation.


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  • MATH 302 - Introduction to Mathematical Reasoning

    (3 units)

    Introduction to logic and methods of proof with applications to elementary set theory, algebra, and combinatorics. Emphasis on mathematical proofs.

    May not be used to satisfy major requirements for either Mathematics or Nevada Teach Secondary Education and Mathematics programs.

    Prerequisite(s): MATH 283  with a “C” or better.

    Grading Basis: Graded
    Units of Lecture: 3
    Offered: Every Fall, Spring, and Summer

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. write cogent proofs using different methods like direct proof, indirect proof, proof by contradiction, proof by induction.
    2. apply combinatorial techniques to prove results about graphs and counting problems.
    3. apply algebraic reasoning to various algebraic structures.


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  • MATH 305 - Functions and Modeling

    (3 units)
    Bridges the math from high school to college calculus through sophisticated interconnections. Prepares teachers to preview college mathematics and its applications in their 7-12 grade classes.

    Prerequisite(s): MATH 182  ; major Nevada Teach Mathematics.

    Grading Basis: Graded
    Units of Lecture: 3
    Offered: Every Spring

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. demonstrate a depth of content knowledge with regard to important secondary mathematics topics such as parametric relations, polar relations, matrices, exponential and logarithmic functions, vectors, and complex numbers.
    2. generate or work with relevant lab or exploration data and use regression, matrix, function pattern, and systems methods to produce a model of the data.
    3. present mathematical ideas and topics in a knowledgeable and effective manner.
    4. demonstrate proficiency in the use of technology in the mathematics classroom.
    5. identify mathematics content connections between the various levels of secondary mathematics curriculum and between secondary- and university-level curriculum.


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  • MATH 310 - Introduction to Analysis I

    (3 units)
    An examination of the theory of calculus of functions of one variable with emphasis on rigorously proving theorems about real numbers, convergence, continuity, differentiation and integration.

    Prerequisite(s): MATH 295  or MATH 301  with a “C” or better.

    Units of Lecture: 3
    Offered: Every Fall and Spring

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. explain and work with the concept of a limit of a sequence and/or a function.
    2. give a precise definition of the continuity and differentiability of a function, and derive various consequences of said properties (such as the Mean Value Theorem or l’Hôpital’s Rule).
    3. use the notion of a limit to test functions for integrability. Integrate functions and derive properties of the Riemann integral.


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  • MATH 311 - Intro To Analysis II

    (3 units)
    Continuation of MATH 310 . Emphasizes proving theorems about series, uniform convergence, functions of several variables: limits, continuity, differentiation, extrema, integration, implicit and inverse function theorems.

    Prerequisite(s): MATH 310  with a “C” or better. Corequisite(s): MATH 330 .

    Units of Lecture: 3
    Offered: Every Fall and Spring

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. write cogent proofs using different methods like direct proof, indirect proof, proof by contradiction, proof by induction.
    2. demonstrate an understanding of the algebraic structure and the topology of Euclidean space.
    3. apply theorems about differentiability and integrability of vector functions of several variables.
    4. test infinite series for convergence.


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  • MATH 320 - Mathematics of Interest

    (3 units)
    Mathematical theory of interest with applications, including accumulated and present value factors, annuities, yield rates, amortization schedules and sinking funds, depreciation, bonds and related securities.

    Prerequisite(s): MATH 176  or MATH 181  with a “C-” or better.

    Units of Lecture: 3
    Offered: Every Fall - Even Years

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. formulate and recognize definitions of interest rate, yield rate, simple and compound interest, the accumulation function, present and future values, force of interest, and equation of value.
    2. write and solve the equation of value given a set of cash flows and interest rate.
    3. demonstrate understanding of basic terminology concerning annuities, loans and cash flows.


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  • MATH 330 - Linear Algebra

    (3 units)
    Vector analysis continued; abstract vector spaces; bases, inner products; projections; orthogonal complements, least squares; linear maps, structure theorems; elementary spectral theory; applications.

    Corequisite(s): MATH 283 .

    Units of Lecture: 3
    Offered: Every Fall, Spring, and Summer

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. compute eigenvalues and eigenvectors; determine whether a matrix is diagonalizable and if possible diagonalize it.
    2. compute the dimension of a vector space, the rank of a matrix or the span of a collection of vectors.
    3. find or identify a basis for a vector space, use the Gram-Schmidt process to find an orthonormal basis, or carry out a change of basis.


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  • MATH 331 - Groups, Rings and Fields

    (3 units)
    Elementary structure of groups, rings and fields, including homomorphisms, automorphisms, normal subgroups, and ideals.

    Prerequisite(s): MATH 295  or MATH 301  with a “C” or better; MATH 330  with a “C” or better.

    Units of Lecture: 3
    Offered: Every Fall

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. demonstrate an understanding of the concepts of group, ring and field and their homomorphisms.
    2. identify irreducible elements in a ring of polynomials.
    3. demonstrate an understanding of cosets in a group, normal subgroups and quotient groups.


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  • MATH 373 - Theory of Positive Integers

    (3 units)
    Mathematical logic, quantifiers, induction, axiomatic development of the theory of positive integers; fundamental theorem of arithmetic. Emphasis is on problem solving and theorem proving.

    Prerequisite(s): MATH 181  with a “C-” or better.

    Units of Lecture: 3
    Offered: Every Spring

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. demonstrate knowledge of the Euclidean division algorithm, divisibility and prime numbers.
    2. solve Diophantine equations and congruences, and use the theory of congruences in applications.
    3. encipher and decipher messages in different encryption systems.?


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  • MATH 381 - Methods of Discrete Mathematics

    (3 units)
    Quantifiers and logical operators; sets, functions, binary relations, digraphs, and trees; inductive definitions, counting techniques, recurrence systems analysis of algorithms, searching and sorting algorithms.

    Prerequisite(s): MATH 182  with a “C-” or better.

    Units of Lecture: 3
    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. manipulate the concepts from set theory of unions, intersections and complements.
    2. use mathematical induction to construct proofs.
    3. demonstrate an understanding of the techniques of counting applied to permutations, combinations.
    4. use graph theory to work with lattices and Boolean algebras.


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  • MATH 401 - Set Theory

    (3 units)
    Formalism, inference, axiomatic set theory, unicity, pairs, relations, functions ordinals, recursive definition, maximality, well ordering, choice, regularity, equinumerosity, cardinal arithmetic.

    Units of Lecture: 3
    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. discuss ZF and ZFC.
    2. demonstrate understanding of the terminology of set theory.
    3. explain concepts and prove facts about ordinals and cardinals.


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  • MATH 410 - Complex Analysis

    (3 units)
    Complex numbers, analytic and harmonic functions. Cauchy-Riemann equations, complex integration, the Cauchy integral formula, elementary conformal mappings. Laurent series, calculus of residues.

    Prerequisite(s): MATH 310  with a “C” or better.

    Units of Lecture: 3
    Offered: Every Fall - Even Years

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. work with holomorphic and harmonic functions.
    2. demonstrate an understanding of the complex logarithm and complex roots.
    3. integrate complex valued functions using residues.


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  • MATH 411 - Real Analysis

    (3 units)
    Continuity, monotonicity, differentiability; uniform convergence and continuity and differentiability; Stone-Weierstrass Theorem; multivariable functions, linear transformations, differentiation, inverse and implicit functions, Jacobians and change of variable; Lebesgue measure and integration.

    Prerequisite(s): MATH 311  and MATH 330 .

    Units of Lecture: 3
    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. distinguish between different modes of convergence.
    2. demonstrate understanding of the Stone Weierstrass theorem.
    3. apply the inverse and implicit function theorems.
    4. demonstrate understanding of the basic theorems of Lebesgue integration.


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  • MATH 412 - Functional Analysis

    (3 units)
    Normed vector spaces, Banach and Hilbert spaces, linear functionals and operators, the Hahn-Banach, closed graph and uniform boundedness theorems with applications, dual spaces, self adjoint operators, compact operators.

    Prerequisite(s): MATH 311  and MATH 330 .

    Units of Lecture: 3
    Offered: Every Spring - Even Years

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. demonstrate an understanding of operators and functionals on Banach spaces and Hilbert spaces.
    2. work with the central concepts and theorems of functional analysis: e.g. the Hahn-Banach theorem, uniform boundedness and open mapping theorems.
    3. apply the spectral theory of bounded self-adjoint operators.


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  • MATH 419 - Topics in Analysis

    (1 to 3 units)
    Variable content chosen from such topics as differential forms, analytic functions, distribution theory, measure and integration, constructive analysis.

    Maximum units a student may earn: 6

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. demonstrate an advanced level of competency in the area of Analysis.


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  • MATH 420 - Mathematical Modeling

    (3 units) CO13, CO14
    Formulation, analysis and critique of methods of mathematical modeling; selected applications in physics, biology, economics, political science and other fields.

    Prerequisite(s): ENG 102 ; CH 201  or CH 202  or CH 203  or CH 212 ; MATH 283  with a “C-” or better; STAT 352  or STAT 461 ; Junior or Senior standing.

    Units of Lecture: 3
    Offered: Every Fall and Spring

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. choose and apply key mathematical and statistical techniques for solving problems in a diverse collection of scientific disciplines.
    2. organize and clean data; critically assess the origin of the data and method of data analysis.
    3. interpret the results of the modeling process to reach sound scientific conclusions within the problem’s economic, scientific, and social context.
    4. propose a project (individually or in a group) and devise strategies and practices to do the research work that will lead, with the support of computational software (e.g. Maple, Mathematica, R, Matlab), to the writing of a technical report using professional typesetting software (e.g., LaTeX).


    Click here for course scheduling information. | Check course textbook information
  

  • MATH 422 - Optimal Analysis

    (3 units)
    Analysis of extrema of real-valued functions and functionals with applications. Introduction to calculus of variations and optimal control.

    Units of Lecture: 3
    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. derive extremal equations and solve some practically important variational problems in single and multiple independent variables including ones with unknown boundary data and integration limits.
    2. solve Isoperimetric and other constrained variational problems using Lagrange multipliers, and apply direct methods to solve variational problems.
    3. apply Hamiltonian principle to derivation of canonical equations and Hamilton-Jacobi equation, and use maximum principle for solution of some optimal control problems.


    Click here for course scheduling information. | Check course textbook information
  

  • MATH 429 - Topics in Applied Analysis

    (1 to 3 units)
    Variable content chosen from such topics as: integral transforms, approximation of functions, nonlinear mathematics, stability theory, matrix exponentials.

    Maximum units a student may earn: 6

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. demonstrate an advanced level of competency in the area of Applied Analysis.


    Click here for course scheduling information. | Check course textbook information
  

  • MATH 430 - Linear Algebra II

    (3 units)
    Vector spaces; duality, direct sums; linear maps: eigenvalues, eigenvectors, rational and Jordan forms; bilinear maps, quadratic forms; inner product spaces: symmetric, skewsymmetric, orthogonal maps, spectral theorem.

    Prerequisite(s): MATH 330 .

    Units of Lecture: 3
    Offered: Every Fall - Odd Years

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. demonstrate understanding of the vocabulary of Linear Algebra at an advanced level.
    2. demonstrate competence at an advanced level by rigorously proving results from Linear Algebra I.
    3. work with self-adjoint, normal and positive operators on inner product spaces.
    4. work with special decompositions and forms of matrices: e.g. the singular value decomposition, Jordan form.


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  • MATH 439 - Topics in Algebra

    (1 to 3 units)
    Variable content chosen from such topics as Galois theory, number theory topological groups, combinatorial analysis, theory of graphs.

    Maximum units a student may earn: 6

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. demonstrate an advanced level of competency in the area of Algebra.


    Click here for course scheduling information. | Check course textbook information
  

  • MATH 440 - Topology

    (3 units)
    General topological spaces, continuity, compact and locally compact spaces, connectedness, path connectedness, product and quotient topologies, countability and separation axioms, metric spaces.

    Prerequisite(s): MATH 310 .

    Units of Lecture: 3
    Offered: Every Spring

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. demonstrate an understanding of topological spaces and continuous functions through proofs and examples.?
    2. analyze topological properties such as compactness, connectedness and path-connectedness, and prove their consequences including the Extreme Value and Intermediate Value Theorem from Calculus.?
    3. analyze continuity or discontinuity of functions defined on a quotient space.


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  • MATH 441 - Intro Algebraic Topology

    (3 units)
    Topological spaces, functors, homotopy, the fundamental group, covering spaces, higher homotopy groups, simplicial complexes, homology theories.

    Prerequisite(s): MATH 440 . Corequisite(s): MATH 331 .

    Units of Lecture: 3
    Offered: Every Fall - Even Years

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. demonstrate understanding of covering spaces for a topological space through proofs and examples.
    2. use functorial properties of homotopy groups to convert topological problems to algebraic ones, in order to solve them.
    3. compute or describe the fundamental group of a topological space by applying the Seifert-van Kampen theorem.


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  • MATH 442 - Differential Geometry

    (3 units)
    Geometry of curves and surfaces in space; Frenet’s formulas; Cartan’s frame fields, Gaussian curvature; intrinsic geometry of surface; congruence of surfaces; the Gauss-Bonnet theorem.

    Prerequisite(s): MATH 311 .

    Units of Lecture: 3
    Offered: Every Fall - Odd Years

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. analyze the intrinsic geometry of curves in space, such as arclength and curvature.
    2. analyze the intrinsic geometry of surfaces in space, such as surface area, Gaussian curvature.
    3. determine whether two surfaces cannot be related by an isometric bijection, due to different intrinsic geometry.
    4. use the Gauss-Bonnet theorem to relate the geometry of an oriented surface without boundary to its topology.


    Click here for course scheduling information. | Check course textbook information
  

  • MATH 443 - Differential Geometry and Relativity I

    (3 units)
    Manifolds, the tangent bundle, differential forms, exterior differentiation, Lie differentiation, Koszul connections, curvature, torsion, Cartan’s structural equations, integration of differential forms.

    Prerequisite(s): MATH 311 .

    Units of Lecture: 3
    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. perform local calculations in differential geometry: covariant derivatives, differential forms, curvature and tensor calculations.?
    2. explain the postulates of General Relativity.
    3. derive geodesic equations in a given spacetime and solve them in special cases.?


    Click here for course scheduling information. | Check course textbook information
  

  • MATH 449 - Topics in Geometry and Topology

    (1 to 3 units)
    Variable content chosen from such topics as differential topology, algebraic topology, convexity, topological vector spaces. Mathematical structures of special relativity.

    Maximum units a student may earn: 6

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. demonstrate an advanced level of competency in geometry and topology.


    Click here for course scheduling information. | Check course textbook information
  

  • MATH 455 - Elementary Theory of Numbers I

    (3 units)
    Congruences, primitive roots, arithmetic functions, quadratic reciprocity, distribution of prime numbers, diophantine equations, rational approximations, algebraic numbers.

    Units of Lecture: 3
    Offered: Every Spring - Odd Years

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. demonstrate knowledge of divisibility, congruences and primitive roots.
    2. solve Diophantine equations using the theory of congruences, diophantine approximation and algebraic numbers.
    3. analyze the distribution of primes and mean values of arithmetic functions.


    Click here for course scheduling information. | Check course textbook information
  

  • MATH 466 - Numerical Methods I

    (3 units)
    Numerical solution of linear systems, including linear programming; iterative solutions of non-linear equations; computation of eigenvalues and eigenvectors, matrix diagonalization. (CS 466 and MATH 466 are cross-listed; credit may be earned in one of the two.)

    Prerequisite(s): MATH 330 .

    Units of Lecture: 3
    Offered: Every Fall

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. implement a numerical method to solve a nonlinear equation: e.g. bisection method, Newton’s method.
    2. solve linear systems using direct and iterative methods.
    3. construct interpolating functions.


    Click here for course scheduling information. | Check course textbook information
  

  • MATH 467 - Numerical Methods II

    (3 units)
    Numerical differentiation and integration; numerical solution of ordinary differential equations, two point boundary value problems; difference methods for partial differential equations. (CS 467 and MATH 467 are cross-listed; credit may be earned in one of the two.)

    Prerequisite(s): MATH 285 .

    Units of Lecture: 3
    Offered: Every Spring

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. use Taylor and Runge-Kutta methods to solve IVP’s for ODE’s.
    2. use the shooting and finite difference methods to solve BVP’s for ODE’s.
    3. use Numerical techniques to solve elliptic, parabolic and hyperbolic PDE’s.


    Click here for course scheduling information. | Check course textbook information
  

  • MATH 475 - Euclidean and Non-Euclidean Geometry

    (3 units)
    Axiom systems, models, independence, consistency; incidence, distance, betweenness, congruence, convexity; inequalities, quadrilaterals, limit triangles, the non-Euclidean geometry of Bolyai-Lobatchevsky.

    Prerequisite(s): MATH 373 .

    Units of Lecture: 3
    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. prove properties of lines, angles, and circles from the Euclidean axioms.
    2. prove properties of lines, angles and circles in non-Euclidean geometry.?
    3. distinguish between geometric properties that depend on the Euclidean parallel postulate and those that are independent of any parallel postulate assumptions.
    4. describe the logical consistency of geometries using models.


    Click here for course scheduling information. | Check course textbook information
  

  • MATH 485 - Graph Theory & Combinator

    (3 units)
    Counting rules; generating functions; recurrence relations; inclusion-exclusion; pigeonhole principle; Ramsey theory; fundamental graph theory concepts (connectedness, coloring, planarity); Eulerian/Hamiltonian chains and circuits; matching.

    Recommended Preparation: MATH 330 .

    Units of Lecture: 3
    Offered: Every Fall

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. solve simple and complex counting problems, by using the addition and product rules, recognizing permutation/combinations with and without replacement, rephrasing as occupancy problems, and/or using the inclusion-exclusion principle/derangements.
    2. demonstrate an understanding of the concept of computational complexity for algorithms, including the use of “Big O” notation.
    3. demonstrate an understanding of the main concepts of graph theory, including graphs versus digraphs, connectedness, graph coloring, planarity, as well as the properties of bipartite graphs, complete graphs, and trees.
    4. demonstrate knowledge of some of the great historical problems and results in graph theory/combinatorics, including the four-color problem, the Konigsberg bridge problem, Euler’s formula, the travelling salesman problem, the hatcheck problem, Kuratowski’s theorem, Ramsey’s theorem, and the solution to the Fibonacci recursion.
    5. make simple “discrete” arguments/proofs, such as using mathematical induction or making “combinatorial arguments”.


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  • MATH 486 - Game Theory

    (3 units)
    Extensive form games; Nash, perfect equilibrium; matrix/bimatrix games; minmax theorem; TU/NTU solutions; marriage, college admissions, and housewrapping games; core; Shapley value; power indices.

    Recommended Preparation: MATH 330 .

    Units of Lecture: 3
    Offered: Every Fall

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. model real world problems from the social and biological sciences as cooperative or noncooperative games, and to choose appropriate solution concepts to analyze them.
    2. solve strategic form matrix and bimatrix games for both minimax solution and Nash equilibria, use backward induction for finding perfect Nash equilibria in perfect-information extensive form games, find the TU solution for bimatrix games, run the Deferred Acceptance Procedure and Top Trading Cycle algorithms for ordinal preference games, and solve for the core and Shapley Value for n-player TU games.
    3. demonstrate an understanding of the underlying theory behind the models, including the minimax theorem, Shapley-Bondareva theorem, Nash’s theorem, the Folk Theorem for repeated games, and the relationship between some of these and linear programming.
    4. demonstrate an understanding of some of the subtleties of game theoretic modelling, such as the role and modelling of information, the advantages and disadvantages of modelling using strategic vs extensive form, the difference between cooperative and noncooperative games, and the implications of the “TU-assumption” for cooperative games.


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  • MATH 487 - Deterministic Operations Research

    (3 units) CO13
    Linear programming and duality theory, integer programming, dynamic programming, PERT scheduling, EOQ inventory model, and nonlinear programming. Emphasis on both theory and applications.

    Prerequisite(s): ENG 102 ; CH 201  or CH 202  or CH 203  or CH 212 ; Junior or Senior standing. Recommended Preparation: MATH 330 .

    Units of Lecture: 3
    Offered: Every Spring

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. use methods of deterministic operations research to model real-world situations, and interpret the results to reach sound conclusions.
    2. communicate, in written form, the results of a model in the context of current thought on the situation being modeled.
    3. distinguish between sound and unsound interpretations of model results applied to issues affecting society.
    4. analyze a problem’s societal context and the impact of context on sound interpretation of mathematical models applied to real-world situations.


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  • MATH 488 - Partial Differential Equations

    (3 units)
    Partial differential equations; first order equations, initial and mixed boundary-value problems for the second order Laplace, heat and wave equations; finite difference approximation.

    Prerequisite(s): MATH 285 .

    Units of Lecture: 3
    Offered: Every Spring

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. apply separation of variables to solve a partial differential equation.
    2. solve second order constant coefficient partial differential equations by applying transforms.
    3. apply the method of characteristics to solve first order partial differential equations.


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  • MATH 490 - Internship

    (1 to 6 units)
    Individual study for the purposes of obtaining credit for high math content work related experience.

    Maximum units a student may earn: 6

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. communicate effectively and professionally and work in teams with colleagues and supervisors in a workplace.
    2. translate business questions and issues into mathematical/statistical problems,?and communicate the technical solutions to the business audience.
    3. practice professional behavior and communications’ standards including verbal and written communication, timeliness, and ethics.


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  • MATH 499 - Independent Study

    (1 to 3 units)
    Individual study conducted under the direction of a faculty member. Limited to 6 credits except under special circumstances.

    Maximum units a student may earn: 3

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. demonstrate an advanced level of competency in the subject of study of this course.


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  • MATH 601 - Set Theory

    (3 units)
    Formalism, inference, axiomatic set theory, unicity, pairs, relations, functions ordinals, recursive definition, maximality, well ordering, choice, regularity, equinumerosity, cardinal arithmetic.

    Units of Lecture: 3
    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. discuss ZF and ZFC.
    2. demonstrate understanding of the terminology of set theory.
    3. explain concepts and prove facts about ordinals and cardinals.


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  • MATH 610 - Complex Analysis

    (3 units)
    Complex numbers, analytic and harmonic functions. Cauchy-Riemann equations, complex integration, the Cauchy integral formula, elementary conformal mappings. Laurent series, calculus of residues.

    Units of Lecture: 3
    Offered: Every Fall - Even Years

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. work with holomorphic and harmonic functions.
    2. demonstrate an understanding of the complex logarithm and complex roots.
    3. integrate complex valued functions using residues.


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  • MATH 611 - Real Analysis

    (3 units)
    Continuity, monotonicity, differentiability; uniform convergence and continuity and differentiability; Stone-Weierstrass Theorem; multivariable functions, linear transformations, differentiation, inverse and implicit functions, Jacobians and change of variable; Lebesgue measure and integration.

    Units of Lecture: 3
    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. distinguish between different modes of convergence.
    2. demonstrate understanding of the Stone Weierstrass theorem.
    3. apply the inverse and implicit function theorems.
    4. demonstrate understanding of the basic theorems of Lebesgue integration.


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  • MATH 612 - Functional Analysis

    (3 units)
    Normed vector spaces, Banach and Hilbert spaces, linear functionals and operators, the Hahn-Banach, closed graph and uniform boundedness theorems with applications, dual spaces, self adjoint operators, compact operators.

    Units of Lecture: 3
    Offered: Every Spring - Even Years

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. demonstrate an understanding of operators and functionals on Banach spaces and Hilbert spaces.
    2. work with the central concepts and theorems of functional analysis: e.g. the Hahn-Banach theorem, uniform boundedness and open mapping theorems.
    3. apply the spectral theory of bounded self-adjoint operators.


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  • MATH 619 - Topics in Analysis

    (1 to 3 units)
    Variable content chosen from such topics as differential forms, analytic functions, distribution theory, measure and integration, constructive analysis.

    Maximum units a student may earn: 6

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. demonstrate an advanced level of competency in the area of Analysis.


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  • MATH 620 - Mathematical Modeling

    (3 units)
    Formulation, analysis and critique of methods of mathematical modeling; selected applications in physics, biology, economics, political science and other fields.

    Units of Lecture: 3
    Offered: Every Fall and Spring

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. choose and apply key mathematical and statistical techniques for solving problems in a diverse collection of scientific disciplines.
    2. organize and clean data; critically assess the origin of the data and method of data analysis.
    3. interpret the results of the modeling process to reach sound scientific conclusions within the problem’s economic, scientific, and social context.
    4. propose a project (individually or in a group) and devise strategies and practices to do the research work that will lead, with the support of computational software (e.g. Maple, Mathematica, R, Matlab), to the writing of a technical report using professional typesetting software (e.g., LaTeX).


    Click here for course scheduling information. | Check course textbook information
  

  • MATH 622 - Optimal Analysis

    (3 units)
    Analysis of extrema of real-valued functions and functionals with applications. Introduction to calculus of variations and optimal control.

    Units of Lecture: 3
    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. derive extremal equations and solve some practically important variational problems in single and multiple independent variables including ones with unknown boundary data and integration limits.
    2. solve Isoperimetric and other constrained variational problems using Lagrange multipliers, and apply direct methods to solve variational problems.
    3. apply Hamiltonian principle to derivation of canonical equations and Hamilton-Jacobi equation, and use maximum principle for solution of some optimal control problems.


    Click here for course scheduling information. | Check course textbook information
  

  • MATH 629 - Topics in Applied Analysis

    (1 to 3 units)
    Variable content chosen from such topics as: integral transforms, approximation of functions, nonlinear mathematics, stability theory, matrix exponentials.

    Maximum units a student may earn: 6

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. demonstrate an advanced level of competency in the area of Applied Analysis.


    Click here for course scheduling information. | Check course textbook information
  

  • MATH 630 - Linear Algebra II

    (3 units)
    Vector spaces; duality, direct sums; linear maps: eigenvalues, eigenvectors, rational and Jordan forms; bilinear maps, quadratic forms; inner product spaces: symmetric, skewsymmetric, orthogonal maps, spectral theorem.

    Units of Lecture: 3
    Offered: Every Fall - Odd Years

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. demonstrate understanding of the vocabulary of Linear Algebra at an advanced level.
    2. demonstrate competence at an advanced level by rigorously proving results from Linear Algebra I.
    3. work with self-adjoint, normal and positive operators on inner product spaces.
    4. work with special decompositions and forms of matrices: e.g. the singular value decomposition, Jordan form.


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  • MATH 639 - Topics in Algebra

    (1 to 3 units)
    Variable content chosen from such topics as Galois theory, number theory topological groups, combinatorial analysis, theory of graphs.

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. demonstrate an advanced level of competency in the area of Algebra.


    Click here for course scheduling information. | Check course textbook information
  

  • MATH 640 - Topology

    (3 units)
    General topological spaces, continuity, compact and locally compact spaces, connectedness, path connectedness, product and quotient topologies, countability and separation axioms, metric spaces.

    Units of Lecture: 3
    Offered: Every Spring

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. demonstrate an understanding of topological spaces and continuous functions through proofs and examples.?
    2. analyze topological properties such as compactness, connectedness and path-connectedness, and prove their consequences including the Extreme Value and Intermediate Value Theorem from Calculus.?
    3. analyze continuity or discontinuity of functions defined on a quotient space.


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  • MATH 641 - Intro Algebraic Topology

    (3 units)
    Topological spaces, functors, homotopy, the fundamental group, covering spaces, higher homotopy groups, simplicial complexes, homology theories.

    Units of Lecture: 3
    Offered: Every Fall - Even Years

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. demonstrate understanding of covering spaces for a topological space through proofs and examples.
    2. use functorial properties of homotopy groups to convert topological problems to algebraic ones, in order to solve them.
    3. compute or describe the fundamental group of a topological space by applying the Seifert-van Kampen theorem.


    Click here for course scheduling information. | Check course textbook information
  

  • MATH 642 - Differential Geometry

    (3 units)
    Geometry of curves and surfaces in space; Frenet’s formulas; Cartan’s frame fields, Gaussian curvature; intrinsic geometry of surface; congruence of surfaces; the Gauss-Bonnet theorem.

    Units of Lecture: 3
    Offered: Every Fall - Odd Years

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. analyze the intrinsic geometry of curves in space, such as arclength and curvature.
    2. analyze the intrinsic geometry of surfaces in space, such as surface area, Gaussian curvature.
    3. determine whether two surfaces cannot be related by an isometric bijection, due to different intrinsic geometry.
    4. use the Gauss-Bonnet theorem to relate the geometry of an oriented surface without boundary to its topology.


    Click here for course scheduling information. | Check course textbook information
  

  • MATH 643 - Differential Geometry and Relativity I

    (3 units)
    Manifolds, the tangent bundle, differential forms, exterior differentiation, Lie differentiation, Koszul connections, curvature, torsion, Cartan’s structural equations, integration of differential forms.

    Units of Lecture: 3
    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. perform local calculations in differential geometry: covariant derivatives, differential forms, curvature and tensor calculations.?
    2. explain the postulates of General Relativity.
    3. derive geodesic equations in a given spacetime and solve them in special cases.?


    Click here for course scheduling information. | Check course textbook information
  

  • MATH 649 - Topics in Geometry and Topology

    (1 to 3 units)
    Variable content chosen from such topics as differential topology, algebraic topology, convexity, topological vector spaces. Mathematical structures of special relativity.

    Maximum units a student may earn: 6

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. demonstrate an advanced level of competency in geometry and topology.


    Click here for course scheduling information. | Check course textbook information
  

  • MATH 655 - Elementary Theory of Numbers I

    (3 units)
    Congruences, primitive roots, arithmetic functions, quadratic reciprocity, distribution of prime numbers, diophantine equations, rational approximations, algebraic numbers. 

    Grading Basis: Graded
    Offered: Every Spring - Odd Years

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. demonstrate knowledge of divisibility, congruences and primitive roots.
    2. solve Diophantine equations using the theory of congruences, diophantine approximation and algebraic numbers.
    3. analyze the distribution of primes and mean values of arithmetic functions.
    4. apply the course concepts to research problems.
    5. synthesize number theoretical methods with other mathematical concepts.


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  • MATH 659 - Special Topics of Interest in Probability

    (1 to 3 units)
    Variable content based on faculty and student interests.

    Maximum units a student may earn: 9

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. demonstrate understanding of the methods discussed in class.
    2. apply methods discussed in class to research questions.
    3. articulate the relationship of methods discussed in class to the broader field of probability and statistics.


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  • MATH 666 - Numerical Methods I

    (3 units)
    Numerical solution of linear systems, including linear programming; iterative solutions of non-linear equations; computation of eigenvalues and eigenvectors, matrix diagonalization. (CS 666 and MATH 666 are cross-listed; credit may be earned in one of the two.)

    Units of Lecture: 3
    Offered: Every Fall

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. implement a numerical method to solve a nonlinear equation: e.g. bisection method, Newton’s method.
    2. solve linear systems using direct and iterative methods.
    3. construct interpolating functions.


    Click here for course scheduling information. | Check course textbook information
  

  • MATH 667 - Numerical Methods II

    (3 units)
    Numerical differentiation and integration; numerical solution of ordinary differential equations, two point boundary value problems; difference methods for partial differential equations. (CS 667 and MATH 667 are cross-listed; credit may be earned in one of the two.)

    Units of Lecture: 3
    Offered: Every Spring

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. use Taylor and Runge-Kutta methods to solve IVP’s for ODE’s.
    2. use the shooting and finite difference methods to solve BVP’s for ODE’s.
    3. use Numerical techniques to solve elliptic, parabolic and hyperbolic PDE’s.


    Click here for course scheduling information. | Check course textbook information
  

  • MATH 675 - Euclidean and Non-Euclidean Geometry

    (3 units)
    Axiom systems, models, independence, consistency; incidence, distance, betweenness, congruence, convexity; inequalities, quadrilaterals, limit triangles, the non-Euclidean geometry of Bolyai-Lobatchevsky.

    Units of Lecture: 3
    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. prove properties of lines, angles, and circles from the Euclidean axioms.
    2. prove properties of lines, angles and circles in non-Euclidean geometry.?
    3. distinguish between geometric properties that depend on the Euclidean parallel postulate and those that are independent of any parallel postulate assumptions.
    4. describe the logical consistency of geometries using models.


    Click here for course scheduling information. | Check course textbook information
  

  • MATH 685 - Graph Theory & Combinator

    (3 units)
    Counting rules; generating functions; recurrence relations; inclusion-exclusion; pigeonhole principle; Ramsey theory; fundamental graph theory concepts (connectedness, coloring, planarity); Eulerian/Hamiltonian chains and circuits; matching.

    Units of Lecture: 3
    Offered: Every Fall

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. solve simple and complex counting problems, by using the addition and product rules, recognizing permutation/combinations with and without replacement, rephrasing as occupancy problems, and/or using the inclusion-exclusion principle/derangements.
    2. demonstrate an understanding of the concept of computational complexity for algorithms, including the use of “Big O” notation.
    3. demonstrate an understanding of the main concepts of graph theory, including graphs versus digraphs, connectedness, graph coloring, planarity, as well as the properties of bipartite graphs, complete graphs, and trees.
    4. demonstrate knowledge of some of the great historical problems and results in graph theory/combinatorics, including the four-color problem, the Konigsberg bridge problem, Euler’s formula, the travelling salesman problem, the hatcheck problem, Kuratowski’s theorem, Ramsey’s theorem, and the solution to the Fibonacci recursion.
    5. make simple “discrete” arguments/proofs, such as using mathematical induction or making “combinatorial arguments”.


    Click here for course scheduling information. | Check course textbook information
  

  • MATH 686 - Game Theory

    (3 units)
    Extensive form games; Nash, perfect equilibrium; matrix/bimatrix games; minmax theorem; TU/NTU solutions; marriage, college admissions, and housewrapping games; core; Shapley value; power indices.

    Units of Lecture: 3
    Offered: Every Fall

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. model real world problems from the social and biological sciences as cooperative or noncooperative games, and to choose appropriate solution concepts to analyze them.
    2. solve strategic form matrix and bimatrix games for both minimax solution and Nash equilibria, use backward induction for finding perfect Nash equilibria in perfect-information extensive form games, find the TU solution for bimatrix games, run the Deferred Acceptance Procedure and Top Trading Cycle algorithms for ordinal preference games, and solve for the core and Shapley Value for n-player TU games.
    3. demonstrate an understanding of the underlying theory behind the models, including the minimax theorem, Shapley-Bondareva theorem, Nash’s theorem, the Folk Theorem for repeated games, and the relationship between some of these and linear programming.
    4. demonstrate an understanding of some of the subtleties of game theoretic modelling, such as the role and modelling of information, the advantages and disadvantages of modelling using strategic vs extensive form, the difference between cooperative and noncooperative games, and the implications of the “TU-assumption” for cooperative games.


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  • MATH 687 - Deterministic Operations Research

    (3 units)
    Linear programming and duality theory, integer programming, dynamic programming, PERT scheduling, EOQ inventory model, and nonlinear programming. Emphasis on both theory and applications.

    Units of Lecture: 3
    Offered: Every Spring

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. use methods of deterministic operations research to model real-world situations, and interpret the results to reach sound conclusions.
    2. communicate, in written form, the results of a model in the context of current thought on the situation being modeled.
    3. distinguish between sound and unsound interpretations of model results applied to issues affecting society.
    4. analyze a problem’s societal context and the impact of context on sound interpretation of mathematical models applied to real-world situations.


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  • MATH 688 - Partial Differential Equations

    (3 units)
    Partial differential equations; first order equations, initial and mixed boundary-value problems for the second order Laplace, heat and wave equations; finite difference approximation.

    Units of Lecture: 3
    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. apply separation of variables to solve a partial differential equation.
    2. solve second order constant coefficient partial differential equations by applying transforms.
    3. apply the method of characteristics to solve first order partial differential equations.


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  • MATH 690 - Internship

    (1 to 6 units)
    Individual study for the purposes of obtaining credit for high math content work related experience. Maximum of 6 credits except under special circumstances.

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. communicate effectively and professionally and work in teams with colleagues and supervisors in a workplace.
    2. translate business questions and issues into mathematical/statistical problems,?and communicate the technical solutions to the business audience.
    3. practice professional behavior and communications’ standards including verbal and written communication, timeliness, and ethics.


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  • MATH 699 - Independent Study

    (1 to 3 units)
    Individual study conducted under the direction of a faculty member. Limited to 6 credits except under special circumstances.

    Maximum units a student may earn: 3

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. demonstrate an advanced level of competency in the subject of study of this course.


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  • MATH 701 - Numerical Analysis and Approximation

    (3 units)
    Norms of vectors and matrices, computation of eigenvalues and eigenvectors, matrix transformations, Weierstrass’ approximation theorem, Chebyshev polynomials, best and uniform approximation, splines, approximation in abstract spaces.

    Units of Lecture: 3
    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. state and prove basic theorems in numerical linear algebra including Schur’s Theorem, quadratic order of convergence of Newton’s methods and the Gershgorin circle theorem.
    2. demonstrate familiarity common algorithms including the shifted QR algorithm of Francis, the algorithms for computation of matrix norms, Gram Schmidt algorithm, Thomas algorithm and Newton’s divided difference formula.
    3. recall and define terminology including error, condition number, matrix norm, machine epsilon, unitary matrix, Haar subspace, order of convergence positive definite matrix and stability.
    4. write practical computer programs.


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  • MATH 702 - Numerical Analysis and Approximation

    (3 units)
    Norms of vectors & matrices, computation of eigen values and eigen vectors, matrix transformations, weierstrass’ approximation theorem, chebyshev polynomials, best and uniform approximation, splines, approximation in abstract spaces.

    Units of Lecture: 3
    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. demonstrate familiarity with the solution of numerical differential equations and understand the classification of PDEs using the terms parabolic, elliptic, and hyperbolic.
    2. study and explain partial differential equations such as Burger’s equation, the non-linear Schroedinger equation and the KdV equation using appropriate numerical algorithms such as Crank-Nicolson, ADI methods, upwind, implicit, explicit, Runge-Kutta, finite differences and psuedo-spectral methods.
    3. demonstrate understanding of concepts such as truncation error, stability, Fourier mode analysis, conserved quantities and dissipation.
    4. state and apply theorems such as the Lax equivalence theorem and the Peano kernel theorem.
    5. demonstrate understanding of algorithmic considerations related to parallel processing and write practical parallel computer programs.


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  • MATH 713 - Abstract and Real Analysis

    (3 units)
    Lebesgue measure, measurable spaces, integration, convergence theorems, Fubini Theorem, measure–theoretic foundations of probability, topological measures, differentiation. Radon-Nikodym Theorem, Riesz Representation, special topics.

    Units of Lecture: 3
    Offered: Every Fall

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. demonstrate understanding of measure theory.
    2. demonstrate understanding of Lebesgue integration.
    3. demonstrate understanding of the uses of modern theories of measure and integration.


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  • MATH 714 - Abstract and Real Analysis

    (3 units)
    Metric spaces, abstract measures, measurable functions, integration, product measures, Fubini Theorem, topological measures, Haar measure, differentiation, Radon-Nikodym Theorem, linear spaces, Hahn-Banach Theorem, Riez Representation

    Units of Lecture: 3
    Offered: Every Spring - Odd Years

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. demonstrate understanding of advanced topics in measure theory.
    2. demonstrate understanding of advanced topics in modern integration.
    3. demonstrate understanding of the relation between integration and differentiation.


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  • MATH 715 - Complex Function Theory

    (3 units)
    Analytic functions, conformal mappings, Cauchy’s theorem, power series, Laurent series, the Riemann mapping theorem, harmonic functions, subharmonic functions, canonical mappings of multiply connected regions, analytical continuation.

    Units of Lecture: 3
    Offered: Every Spring - Even Years

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. demonstrate knowledge and understanding of the topics listed in the course description and their applications in pure and applied mathematics.


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  • MATH 716 - Complex Function Theory

    (3 units)
    Analytic functions, conformal mappings, Cauchy’s theorem, power series, Laurent series, the Riemann mapping theorem, harmonic functions, subharmonic functions, canonical mappings or multiple connected regions, analytical continuation.

    Units of Lecture: 3
    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. demonstrate knowledge and understanding of the topics listed in the course description and their applications in pure and applied mathematics.


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  • MATH 721 - Nonlinear Dynamics and Chaos I

    (3 units)
    Geometric approach to nonlinear dynamics, Poincare maps, center manifolds, normal forms, averaging method.

    Units of Lecture: 3
    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. demonstrate an advanced level of competency in geometric approach to 1 and 2- dimensional flows, stability analysis, Lyapunov stability and Lyapunov function method, classification and analysis of bifurcation of equilibria in 1 and 2-dimentional flows, conservative, reversible and dissipative systems, index theory.
    2. demonstrate an advanced level of competency in application of Poincare-Bendixon theorem, Lienard system, Hopf bifurcations, global bifurcation of cycles, hyperbolic systems.
    3. demonstrate an advanced level of competency in asymptotic methods, weakly coupled nonlinear oscillators, synchronization phenomena in nonlinear systems and real world models.


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  • MATH 722 - Nonlinear Dynamics and Chaos II

    (3 units)
    Local bifurcations of vector fields, bifurcations of maps, global bifurcations and chaos, Milnikov’s method, chaotic attractors, applied chaos.

    Units of Lecture: 3
    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. demonstrate an advanced level of competency in center manifold and normal forms theorie, applications of normal forms theory to analysis of local bifurcations in multidimensional systems, normal forms and bifurcations in periodic systems.
    2. demonstrate knowledge of theory and applications of Lorenz’s and Rossler’s systems, chaotic attractors, Lyapunov’s exponents, Eegodicity concept.
    3. demonstrate an advanced level of competency in nonlinear maps and their bifurcations, normal form theory for nonlinear maps, chaotic dynamics of maps.


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  • MATH 731 - Modern Algebra

    (3 units)
    Groups, fields, linear dependence, linear transformations, Galois theory.

    Units of Lecture: 3
    Offered: Every Fall - Odd Years

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. demonstrate an advanced level of competency in the theory of rings (ideals, factorization in commutative rings, localization, rings of polynomials and of power series).
    2. demonstrate an advanced level of competency in the theory of modules (exact sequences, projective and injective modules, modules over principal ideal domains).
    3. demonstrate an advanced level of competency in linear algebra (determinants, rational canonical form, Jordan canonical form, minimal and characteristic polynomials, eigenvalues and eigenvectors).


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  • MATH 732 - Modern Algebra

    (3 units)
    Groups, fields, linear dependence, linear transformations, Galois theory.

    Units of Lecture: 3
    Offered: Every Spring - Even Years

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. demonstrate an advanced level of competency in Galois theory (field extensions, splitting fields, algebraic closure, normality, Galois group of a polynomial, finite fields,separability, cyclotomic extensions, radical extensions).
    2. demonstrate an advanced level of competency in commutative algebra (chain conditions, prime and primary ideals, primary decomposition, Jacobson radical, Hilbert Nullstellensatz).


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  • MATH 741 - Topology

    (3 units)
    Topological structures, uniform spaces, metric spaces, compact and locally compact spaces, connectivity, function spaces, topological algebra, elementary homological algebra, singular homology theory, cell complexes, homotopy groups.

    Units of Lecture: 3
    Offered: Every Fall - Even Years

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. compute the homology of a space defined by a simplicial complex.
    2. use homotopy groups or homology groups to demonstrate that spaces are not homeomorphic to one another.
    3. apply homological algebraic arguments to prove results about continuous maps between spaces.


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  • MATH 742 - Topology

    (3 units)
    Topological structures, uniform spaces, metric spaces, compact and locally compact spaces, connectivity, function spaces, topological algebra, elementary homological algebra, singular homology theory, cell complexes, homotopy groups.

    Units of Lecture: 3
    Offered: Every Spring - Odd Years

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. use long exact sequences to compute homology and cohomology groups of topological spaces.
    2. compute homology groups and cohomology groups of a space from the Mayer Vietoris sequence for a decomposition into subspaces.
    3. use the Kunneth formula to determine the cohomology of a product space. 


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  • MATH 751 - Operations Research I

    (3 units)
    Theoretical optimization theory; linear programming, simplex method convexity, duality theory, integer and fractional programming algorithms, Kuhn-Tucker theory, linear complementary problem, Lemke’s algorithm.

    Units of Lecture: 3
    Offered: Every Fall - Even Years

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. demonstrate understanding of and facility with all of the mathematical details of the simplex algorithm for solving linear programs, duality theory, and a linear algebraic approach to sensitivity analysis for linear programs, including being able to formally prove results in these areas.
    2. demonstrate understanding of and facility with extensions of the simplex algorithm to solve nonlinear problems, such as integer programming, fractional programming, and linear complementarity problems.
    3. demonstrate understanding of the Kuhn Tucker conditions for nonlinear programming, how they are related to optimality conditions for certain optimization problems, and how to use them to solve certain convex and non-convex problems.


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  • MATH 752 - Operations Research II

    (3 units)
    A survey of stochastic operations research: decision analysis, reliability theory, Markov chains, queuing theory, stochastic inventory theory.

    Units of Lecture: 3
    Offered: Every Fall - Odd Years

    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. set up, model, and solve real world problems from the business and non-business world as problems in decision analysis, reliability theory, queuing theory, or stochastic inventory theory.
    2. demonstrate knowledge of the mathematical theories of: decision analysis, risk theory, reliability theory (including models with a true time component), Markov Chains, birth-death processes (especially queues), and stochastic inventory theory.


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  • MATH 761 - Methods in Applied Math I

    (3 units)
    Finite dimensional Vector Spaces, Function Spaces, Integral Equations, Greens Functions, Differential Operators.

    Units of Lecture: 3
    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. demonstrate understanding of finite dimensional vector spaces and function spaces through proofs and examples.
    2. determine analytical solutions for certain classes of linear integral equations, and apply Greens function methodologies to solve the problems formulated in the area of partial differential equations.
    3. set up, analyze and solve problems arising in various application domains using methodologies they will study in this course.


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  • MATH 762 - Methods in Applied Math II

    (3 units)
    Calculus of Variations, Complex Variables, Transform and Spectral Theory, Partial Differential Equations, Asymptotics, Perturbation Theory.

    Units of Lecture: 3
    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. demonstrate ability to solve problems using calculus of variations and complex variables methodology.
    2. demonstrate competence at the advanced level in application of spectral and integral transform methodologies, and perturbation theory to analysis and approximating of solutions of partial differential equations.
    3. apply these methodologies to solving practically important problems from various applied fields and interpret the solutions using analytical and numerical approaches.


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  • MATH 773 - Topics in Algebra

    (3 units)
    Variable content chosen from such topics as theory of equations, number theory, and groups and permutations.

    Maximum units a student may earn: 9

    Units of Lecture: 3
    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. demonstrate an advanced level of competency in Algebra.


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  • MATH 774 - Topics in Geometry and Analysis

    (3 units)
    Variable content chosen from such topics as plane algebraic curves, theory of surfaces, pseudo-Euclidean spaces. May be repeated when course content differs.

    Maximum units a student may earn: 9

    Units of Lecture: 3
    Student Learning Outcomes
    Upon completion of this course, students will be able to:
    1. demonstrate an advanced level of competency in geometry and analysis.


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