






MATH 1000  How to Conquer Math












Units: 

1 units




Course Components 









This course is designed for the mathematics student who either suffers from a selfreported case of mathemaphobia or is simply interested in understanding the phenomenon to better teach mathematics. Through selfreflection, practice of mathematics skills, practice of testtaking skills, reading thought process surrounding mathematics, students will gain confidence, understanding and problemsolving skills.







MATH 1010  Intermediate Algebra












Units: 

4 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in (MATH 980 OR MATH 990) OR Accuplacer EA score of 54 or better OR ACT Math score of 18 or better OR SAT Math score of 470 or better.









Rapid review of elementary algebra; linear equations and inequalities, systems of linear equations; exponents, radicals, complex numbers, exponentials, logarithms; solving polynomial, rational, radical exponential and logarithmic equations; applications throughout these topics.







MATH 1030  Introduction to Quantitative Reasoning












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in (MATH 980 OR MATH 1010) OR Accuplacer EA score of 60 or better OR ACT Math score of 19 or better OR SAT Math score of 500 or better.


Requirement Designation 

Quantitative Reasoning (Math)









This course helps students learn how to use some simple mathematical techniques effectively in their own field of study and apply those concepts to practical, reallife situations. Topics covered: sets and Venn diagrams, different systems of units and unit conversions, using percents and estimations, financial mathematics involved in loans and investments, linear and exponential modeling and applications, geometric measurements and scaling. This course is primarily for undergraduate students who will not take any further mathematics, except for statistics/probability.







MATH 1040  Introduction to Statistics and Probability












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in (MATH 980 OR MATH 1010 OR MATH 1030 OR MATH 1050 OR MATH 1070 OR MATH 1080 OR MATH 1090) OR Accuplacer CLM score of 50 or better OR ACT Math score of 22 or better OR SAT Math score of 550 or better.


Requirement Designation 

Quantitative Reasoning (Statistics/Logic)









Topics covered: how to collect, organize, analyze, display, and interpret data; deviation, variance and standard deviation, Empirical rule; basic concepts of probability and counting, conditional probability, multiplication and addition rule; probability distributions, binomial distributions; standard normal (bellshaped) distributions; correlation and linear regression.







MATH 1050  College Algebra












Units: 

4 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in (MATH 1010 OR MATH 1060 OR MATH 1080 OR MATH 1090) OR Accuplacer CLM score of 60 or better OR ACT Math score of 23 or better OR SAT Math score of 570 or better.


Requirement Designation 

Quantitative Reasoning (Math)









Functions, inverses and graphs; polynomial, rational, radical, exponential and logarithmic functions; systems of equations and matrices; applications; arithmetic and geometric sequences and series.







MATH 1060  Trigonometry












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 1050 OR Accuplacer CLM score of 80 or higher.


Requirement Designation 

Quantitative Reasoning (Math)









Trigonometric functions, inverses, equations and identities with applications; introduction to vectors. It is strongly recommended that students complete Math 1050 (College Algebra) before taking Math 1060.







MATH 1070  Introduction to Statistical Inference












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in (MATH 1010 OR MATH 1030 OR MATH 1040 OR MATH 1050 OR MATH 1080 OR MATH 1090) OR "B" or better in MATH 980 OR Accuplacer CLM score of 50 or better OR ACT Math score of 22 or better OR SAT Math score of 550 or better.


Requirement Designation 

Quantitative Reasoning (Statistics/Logic)









The important topics used in making inferences from data will be presented and illustrated. As well as material on descriptive statistics, estimation of the mean, or of the proportion, in one or two populations, simple linear regression, and oneway analysis of variance are covered.







MATH 1080  Precalculus












Units: 

5 units




Course Components 










Enrollment Requirement 

Prerequisites: "B" or better in (MATH 1010 OR MATH 1050 OR MATH 1060) OR Math ACT score of at least 24 OR Math SAT score of at least 580 OR Accuplacer CLM score of 65 or better OR Department Consent.


Requirement Designation 

Quantitative Reasoning (Math)









Provides indepth and accelerated review of college algebra and trigonometry to prepare for sciencetrack calculus courses. Most topics from MATH 1050 and MATH 1060 are covered in this course.







MATH 1090  Business Algebra












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in (MATH 1010 OR MATH 1050 OR MATH 1080) OR Accuplacer CLM score of 60 or better OR ACT Math score of 23 or better OR SAT Math score of 570 or better.


Requirement Designation 

Quantitative Reasoning (Math)









Functions and graphs, polynomial and rational functions, matrices, Gaussian elimination, exponential and logarithmic functions, growth, periodic and continuously compounded interest, arithmetic and geometric series, annuities and loans.







MATH 1100  Business Calculus












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in (MATH 1050 OR MATH 1080 OR MATH 1090 OR MATH 1210) OR Accuplacer CLM score of 80 or better OR ACT Math score of 28 or better OR SAT Math score of 650 or better.


Requirement Designation 

Quantitative Reasoning (Math & Stat/Logic)









Introduction to limits. Differentiation and integration of polynomial, rational, logarithmic and exponential function. Optimization of functions, including business applications such as marginal analysis. Business applications of the derivative and integral. Brief exposure to partial derivatives and functions of several variables. (Not for students who have completed more than one semester of calculus).







MATH 1170  Calculus for Biologists I












Units: 

4 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in ((MATH 1050 AND MATH 1060) OR MATH 1080 OR (MATH 1060 AND Accuplacer CLM score of 80+) OR MATH 1210 OR MATH 1310) OR AP Calc AB score of 3+ OR Accuplacer CLM score of 90+ OR ACT Math score of 28+OR SAT Math score of 650+.


Requirement Designation 

Quantitative Reasoning (Math & Stat/Logic)









Derivation of dynamical models of biological systems and their analysis with differential and integral calculus. Discretetime dynamical systems for growth, breathing, selection, the heart, etc. Differentiation and its applications to stability, approximation of functions, maximization, and limits. Differential equations describing growth, diffusion, and selection, and their solution with integral calculus. Computer lab using Maple.







MATH 1180  Statistics with Calculus for Biologists












Units: 

4 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 1170.


Requirement Designation 

Quantitative Reasoning (Math & Stat/Logic)









Probabilistic models of biological systems and their analysis. Derivation and analysis of stochastic dynamical systems describing growth, diffusion, and selection. Introduction to probability theory including distributions, random variables, and probability density functions. Applications of binomial, exponential, Poisson, and normal distributions. Statistical methods including parameter estimation, maximum likelihood, hypothesis testing and regression. Computer lab using Maple.







MATH 1210  Calculus I












Units: 

4 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in (((MATH 1050 AND 1060) OR MATH 1080 OR (MATH 1060 AND Accuplacer CLM score of 80+)) OR AP Calc AB score of 3+ OR Accuplacer CLM score of 90+ OR ACT Math score of 28+ OR SAT Math score of 650+.


Requirement Designation 

Quantitative Reasoning (Math & Stat/Logic)









Functions and their graphs, differentiation of polynomial, rational and trigonometric functions. Velocity and acceleration. Geometric applications of the derivative, minimization and maximization problems, the indefinite integral, and an introduction to differential equations. The definite integral and the Fundamental Theorem of Calculus.







MATH 1220  Calculus II












Units: 

4 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in (MATH 1210 OR MATH 1250 OR MATH 1270 OR MATH 1311 OR MATH 1310) OR AP Calculus AB score of at least 4 OR AP Calculus BC score of at least 3.


Requirement Designation 

Quantitative Reasoning (Math & Stat/Logic)









Geometric applications of the integral, logarithmic, and exponential functions, techniques of integration, conic sections, improper integrals, numerical approximation techniques, infinite series and power series expansions, differential equations (continued).







MATH 1250  Calculus for AP Students I












Units: 

4 units




Course Components 










Enrollment Requirement 

Prerequisites: AP Calculus AB score of at least 4 OR AP Calculus BC score of at least 3.


Requirement Designation 

Quantitative Reasoning (Math & Stat/Logic)



Honors Course









MATH 1250 and MATH 1260 together replace the three semester sequence MATH 1210, MATH 1220, MATH 2210. Review of introductory calculus, applications of differential and integral calculus, introduction to differential equations, conic sections and polar coordinates, numerical approximation, sequences and series, power series.







MATH 1260  Calculus for AP Students II












Units: 

4 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 1250 OR AP Calculus BC score of at least 4.


Requirement Designation 

Quantitative Reasoning (Math & Stat/Logic)



Honors Course









Completion of MATH 1260 is equivalent to completing the entire threesemester Calculus I, II, III sequence. Vectors in the plane and in 3space, differential calculus in several variables, integration and its applications in several variables, vector fields, and line, surface and volume integrals. Green's and Stokes' Theorems.







MATH 1310  Engineering Calculus I












Units: 

4 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in ((MATH 1050 AND 1060) OR MATH 1080 OR (MATH 1060 AND Accuplacer CLM score of 80+)) OR AP Calc AB score of 3+ OR Accuplacer CLM score of 90+ OR ACT Math score of 28+ OR SAT Math score of 650+ OR Department Consent.


Requirement Designation 

Quantitative Reasoning (Math & Stat/Logic)









Differential and integral calculus with a focus on engineering applications and projects: functions and models; rates of change in science and engineering, limits and derivatives; related rates; derivatives and shapes of graphs; optimization; Newton's method; definite integrals, antidifferentiation and Fundamental Theorem of Calculus; techniques of integration; numerical and symbolic integration with software; arclength, area and volumes via integration.







MATH 1311  Accelerated Engineering Calculus I












Units: 

4 units




Course Components 










Enrollment Requirement 

Prerequisites: AP Calculus AB score of 4 or better OR AP Calc BC score of 3 or better.


Requirement Designation 

Quantitative Reasoning (Math & Stat/Logic)



Honors Course









Math 1311 and 1321 together are equivalent to the three semester sequence Math 1210, Math 1220, and Math 2210. This sequence is intended for engineering majors. Review of introductory calculus, applications of differential and integral calculus, introduction to differential equations, conic sections and polar coordinates, numerical approximation, sequences and series, power series.







MATH 1320  Engineering Calculus II












Units: 

4 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 1310 OR AP Calc BC score of 3 or better OR Department Consent.


Requirement Designation 

Quantitative Reasoning (Math & Stat/Logic)









Differential and Integral Calculus II, with a focus on applications and projects for engineers: integral expressions for moments, centers of mass, and work; modeling with first order differential equations; infinite series and sequences; power series and Taylor series; vectors, dot and cross products, and the geometry of space; the calculus of vector functions and particle motion in space; differential calculus for functions of several variables, including linear approximation, partial and directional derivatives, chain rule, and multivariable optimization.







MATH 1321  Accelerated Engineering Calculus II












Units: 

4 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 1311 OR AP Calculus BC score of 4 or better.


Requirement Designation 

Quantitative Reasoning (Math & Stat/Logic)



Honors Course









Completion of Math 1321 is equivalent to completing the entire three semester Calculus I, II, III sequence. Vectors in the plane and in 3space, differential calculus in several variables, integration and its applications in several variables, vector fields, and line, surface and volume integrals, Green's and Stokes Theorems.







MATH 1900  Topics in Mathematics












Units: 

1  4 units




Course Components 










Enrollment Requirement 

Instructor's Consent.









Various special topics in mathematics to be treated at the appropriate level.







MATH 2015  Algebraic Reasoning












Units: 

4 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 1010 OR Accuplacer CLM score of 60 or better OR ACT Math score of 23 or better OR SAT Math score of 570 or better.


Requirement Designation 

Quantitative Reasoning (Math)









Although the study of algebra and functions generally begins at the middle and continues through high school grades, many core concepts and practices are accessible at a much earlier age. In fact, if the students are to be successful in algebra their teachers in early grades have to be cognizant and knowledgeable of what those concepts are and how they develop. The purpose of this course is to extend the concepts of number sense (which for some students will have been enriched in Math4010) and develop algebraic reasoning skills of the future elementary school teachers or anyone in a major that doesn't require precalculus. Prerequisites for this course expire after one year.







MATH 2090  Teaching Secondary School Math for Elementary Teachers












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in (MATH4020 AND (MATH1210 OR MATH1220 OR MATH1250 OR MATH1260 OR MATH1270 OR MATH1311 OR MATH1280 OR MATH1321 OR MATH1310 OR MATH1320 OR MATH2210 OR AP Calc AB score of at least 4 OR AP Calc BC score of at least 3)).









Meets with 4090. In this course we discuss teaching methods for secondary classroom, including appropriate use technology. Important components are developing topics across the curriculum, connections between mathematical concepts, as well as other important issues in running one's classroom: setting norms, goals, assessing students work and knowledge, providing practice and direction, managing diverse populations. This is a hands on class with ample opportunities for teaching. First session course.







MATH 2200  Introduction to Discrete Mathematics












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in (MATH 1220 OR MATH 1250 OR MATH 1260 OR MATH 1270 OR MATH 1311 OR MATH 1320 OR MATH 1321 OR MATH 2210) OR AP Calc BC score of 5.









Fundamentals of logic, set theory, order, relations, functions. Elementary number theory, modular arithmetic. Combinatorics; counting permutations, generating functions, matrix operations. Basic algebraic structures; groups, rings. Discrete probability. Introduction to graph theory, trees, search optimization problems. Boolean algebra.







MATH 2210  Calculus III












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in (MATH 1220 OR MATH 1250 OR MATH 1320) OR AP Calculus BC score of at least 4.


Requirement Designation 

Quantitative Reasoning (Math & Stat/Logic)









Vectors in the plane and in 3space, differential calculus in several variables, integration and its applications in several variables, vector fields and line, surface, and volume integrals. Green's and Stokes' theorems.







MATH 2250  Differential Equations and Linear Algebra












Units: 

4 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in (MATH 2210 OR MATH 1260 OR MATH 1280 OR MATH 1321 OR MATH 1320 OR ((MATH 1220 OR MATH 1250 OR MATH 1270 OR MATH 1311 OR AP Calculus BC score of 5) AND PHYS 2210 OR PHYS 3210)).


Requirement Designation 

Quantitative Reasoning (Math & Stat/Logic)









This is a hybrid course which teaches the allied subjects of linear algebra and differential equations. These topics underpin the mathematics required for most students in the Colleges of Science, Engineering, Mines & Earth Science.







MATH 2270  Linear Algebra












Units: 

4 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in (MATH 2210 OR MATH 1260 OR MATH 1280 OR MATH 1321 OR MATH 1320).


Requirement Designation 

Quantitative Reasoning (Math & Stat/Logic)









Euclidean space, linear systems, Gaussian elimination, determinants, inverses, vector spaces, linear transformations, quadratic forms, least squares and linear programming, eigenvalues and eigenvectors, diagonalization. Includes theoretical and computer lab components.







MATH 2280  Introduction to Differential Equations












Units: 

4 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 2270.


Requirement Designation 

Quantitative Reasoning (Math & Stat/Logic)









Linear and nonlinear differential equations and systems of equations, with applications. Matrix exponential, fundamental solution matrix, phasespace and portraits, stability, initial and boundaryvalue problems, introduction to partial differential equations. Requires familiarity with linear algebra. Includes theoretical and computer lab components.







MATH 3000  Undergraduate Colloquium












Units: 

1 units




Course Components 









Colloquium of presentations of topics of contemporary mathematical interest.







MATH 3010  Topics in the History of Mathematics












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in (MATH 1210 OR MATH 1250 OR MATH 1270 OR MATH 1310 OR MATH 1311 OR MATH 1220 OR MATH 1320 OR MATH 1321 OR MATH 2210) OR AP Calculus AB score of at least 4 OR AP Calculus BC score of at least 3.


Requirement Designation 

Comm/Wrtg & Phys/Life Sci Exploration









A brief look at the history of mathematics, focusing on the principal ideas of importance in the development of the subject.







MATH 3070  Applied Statistics I












Units: 

4 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in (MATH 1220 OR MATH 1250 OR MATH 1270 OR MATH 1311 OR MATH 1320 OR MATH 1321) OR AP Calculus BC score of at least 4.


Requirement Designation 

Quant Reason(Math & Stat/Log) & Quant Intensive BS









An introduction to basic probability theory, sampling from normal populations, largesample problems, sampling from one or two populations, estimation, and testing. R is used to perform statistical analyses. There are three lectures and one 1 1/2 hour lab per week.







MATH 3080  Applied Statistics II












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 3070.


Requirement Designation 

Quant Reason(Math & Stat/Log) & Quant Intensive BS









Introduction to analysis of variance, regression analysis, correlation analysis, and nonparametric techniques. Continued use of R programming language. There are two lectures and one 1 1/2 hour lab per week.







MATH 3100  Foundations of Geometry












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 2200 AND (MATH 2210 OR MATH 1260 OR MATH 1280 OR MATH 1321 OR MATH 3140).


Requirement Designation 

Quantitative Reasoning (Math & Stat/Logic)









Modern axiomatic development of Euclidean geometry and of trigonometry, also incidence theorems, projective invariants, straightedge and compass constructions, spherical and hyperbolic geometries.







MATH 3140  Vector Calculus and Partial Differential Equations for Engineers












Units: 

4 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in ((MATH 2250 AND (MATH 1320 OR MATH 1321 OR MATH 2210 OR MATH 1260)) OR MATH 2280).









Integration and its applications in several variables, vector fields and line, surface, and volume integrals. Green's and Stokes' theorems. Fourier series and boundaryvalue problems for the wave, heat, and Laplace equations, separation of variables.







MATH 3150  Partial Differential Equations for Engineering Students












Units: 

2 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in ((MATH 2250 OR (MATH 2270 AND MATH 2280) AND (MATH 2210 OR MATH 1260 OR MATH 1280 OR MATH 1321)).









Fourier series and boundaryvalue problems for the wave, heat, and Laplace
equations, separation of variables in rectangular and radial geometries,
Fourier transform.







MATH 3160  Applied Complex Variables












Units: 

2 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 2250 OR (MATH 2270 AND MATH 2280).









Analytic functions, complex integration, Cauchy integral theorem, Taylor and Laurent series, residues and contour integrals, conformal mappings with applications to electrostatics, heat, and fluid flow.







MATH 3170  R Lab I












Units: 

1 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in (MATH 1220 OR MATH 1250 OR MATH 1270 OR MATH 1311 OR MATH 1320) OR AP Calculus BC score of at least 4.









For students who wish to participate only in the Lab component of MATH 3070.







MATH 3180  R Lab II












Units: 

1 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 3070 OR MATH 3170.









For students who wish to participate only in the Lab component of MATH 3080.







MATH 3210  Foundations of Analysis I












Units: 

4 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in ((MATH 2210 OR MATH 1260 OR MATH 1280 OR MATH 1321 OR MATH 3140) AND (MATH 2200 OR MATH 2270 OR MATH 2250)).


Requirement Designation 

Quant Reason(Math & Stat/Log) & Quant Intensive BS



Honors Course









Logic, methods of proof and mathematical argument in mathematical analysis. Rigorous reconsideration of the realnumber system, infinite series and of continuity, differentiation and integration for functions of one variable. The emphasis is on improving the student's ability to understand and explain concepts in a logical and complete manner.







MATH 3220  Foundations of Analysis II












Units: 

4 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 3210.


Requirement Designation 

Quant Reason(Math & Stat/Log) & Quant Intensive BS



Honors Course









Advanced multivariable calculus. Topics include continuity, compactness, differentiation and affine approximation, chain rule, Taylor series, extremization, error estimation, inverse and implicit function theorems, Riemann integration, Fubini's Theorem, change of variables formula. The emphasis is on further developing the student's ability to understand more abstract concepts and to write an effective and rigorous mathematical argument.







MATH 3600  The Role of Mathematics in Medicine












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: ((AP Calc AB score of 3+ OR ACT Math score of 28+ OR SAT score of 630+ OR Accuplacer CLM score of 95+ OR "C" or better in (MATH 1050 AND 1060) OR MATH 1080) OR (BIOL 2010 OR 2020 OR 2030)) AND Instructor Consent.









Meets with BIOL 5400. This course will develop 12 detailed case studies where mathematics has played a fundamental role in improving medical care. Each week will begin with the medical and biological background, showing both the underlying physiology and the medical problem, then move on to how mathematical or quantitative methods changed practice. Students will learn the underlying mathematical methods from the ground up, program simple simulations on the computer, and use the mathematics and computer simulations to evaluate the medical implications of different therapies or control measures. It is recommended that MATH 1170 or 1210 be completed prior to enrolling in this course.







MATH 3900  Topics in Mathematics












Units: 

1  4 units





Laboratory


Special Topics



Course Components 










Enrollment Requirement 

Prerequisites: Instructor Consent.









Various special topics in mathematics to be treated at the appropriate level.







MATH 4010  Mathematics for Elementary School Teachers I












Units: 

4 units




Course Components 










Enrollment Requirement 

Prerequisites: "B" or better in (MATH 1010 OR MATH 1050) OR Accuplacer CLM score of at least 65 OR ACT Math score of at least 24 OR SAT Math score of at least 580.


Requirement Designation 

Quant Reason(Math & Stat/Log) & Quant Intensive BS









This is the first course in a twocourse sequence for prospective elementary school teachers. This is a content course that provides teachers with a deeper understanding of the real number system and arithmetic operations for whole numbers, fractions, and decimals. This provides the conceptual framework that allows teachers to analyze and correct common student misunderstandings in Grades K6.
See the Utah State Core Curriculum at www.usoe.k12.ut.us.
Teaching methods pertaining to this material are discussed in EDU 5360.
Prerequisites for this course expire after two years.







MATH 4020  Mathematics for Elementary School Teachers II












Units: 

4 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in (MATH 4010 AND (MATH 4015 OR MATH 1050)).


Requirement Designation 

Quant Reason(Math & Stat/Log) & Quant Intensive BS









This is a continuation of MATH 4010, but deals with a different part of the mathematics curriculum. It is a content course that gives teachers a better understanding of topics in geometry appropriate to Grades K6, including measurement, symmetry, geometric shapes, congruence and similarity. The course presents ideas from an intuitive perspective that prepares teachers to discuss geometry with children, and from a computational perspective to enable teachers to work with students to calculate distance, area and volume in both customary and metric units, measure angles, construct figures, and more. A brief discussion of topics in statistics and probability for Grades K6 is also included. See the Utah State Core Curriculum at www.usoe.k12.ut.us. Teaching methods pertaining to this material are discussed in EDU 5360. Prerequisites for this course expire after one year.







MATH 4030  Foundations of Algebra












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 2200 AND (MATH 2210 OR MATH 1260 OR MATH 1280 OR MATH 1321 OR MATH 3140).


Requirement Designation 

Quant Reason(Math & Stat/Log) & Quant Intensive BS









The integers, unique factorization, and modular arithmetic. Polynomial rings. Introduction to abstract algebraic systems.







MATH 4090  Teaching of Secondary School Mathematics












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in (MATH 3100 AND MATH 4030).
Corequisites: "C" or better in MATH 4095.


Requirement Designation 

Quantitative Reasoning (Math & Stat/Logic)









Meets with MATH 2090. In this course we discuss teaching methods for secondary classroom, including appropriate use of technology. Important components are developing topics across the curriculum, connections between mathematical concepts, as well as other important issues in running one's classroom: setting norms, goals, assessing students work and knowledge, providing practice and direction, managing diverse populations. This is a hands on class with ample opportunities for teaching. First session course.







MATH 4095  Practicum for Secondary Mathematics Teachers












Units: 

2 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 3100 AND MATH 4030.
Corequisite: MATH 4090.









This is a practicum course that will parallel MATH 4090. One purpose of this course is to help students develop an awareness of meaningful ways to teach geometry and algebra to students in the 7th through 12th grades. Another purpose of this course is to help students become reflective teachers who can look critically at textbooks, teaching materials, assessments and their own teaching for the purpose of better meeting the needs of students. This course will have a strong student teaching component.







MATH 4100  Introduction to Data Science












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in (MATH 1170 OR MATH 1210 OR MATH 1250 OR MATH 1310 OR MATH 1311) OR AP AB Calculus score of 4 or higher OR AP Calculus BC score of 3 or higher.


Requirement Designation 

Quantitative Intensive BS









The course begins by bootstrapping student's coding skills in the programming language Python, followed by a review of the relevant concepts from statistics. After that, we will move through a series of data science methods using reallife, projectbased, lectures and computer labs.Â The major goals of this course are to learn how to use tools for acquiring, cleaning, analyzing, exploring, and visualizing data; making datadriven inferences and decisions; and effectively communicating results. These will be accomplished through an indepth sequence of topics which will introduce students to the following data preparation and analysis methods: Acquiring data through webscraping and data APIs, Cleaning and reshaping messy datasets using methods such as data frames, regular expressions or dedicated tools, Exploratory data analysis and visualization, Hypothesis testing, Clustering and classification, Rating and ranking, Recommendations, Network analysis, Regression and statistical inference, Natural language processing, Working with large data: databases, parallel programming. A major component of this course will be learning how to use pythonbased programming tools to apply these methods to reallife datasets. Students should have a basiclevel of programming experience before taking this course.







MATH 4190  Mathematics Teaching Internship












Units: 

1  3 units




Course Components 










Enrollment Requirement 

Prerequisites: Department Consent.









Attend Intermediate Algebra course, assist in grading, teach a weekly review session, meet weekly to discuss pedagogy and evaluations of teaching.







MATH 4200  Introduction to Complex Variables












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 3220.


Requirement Designation 

Quantitative Reasoning (Math & Stat/Logic)



Honors Course









Complex functions and their differentiability, complex integrals, power series, the Cauchy theorem and formulas, residues and applications to evaluating integrals, conformal mappings and applications. Graduate students who need this course should consult the instructor.







MATH 4400  Introduction to Number Theory












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 2270 OR MATH 2250.


Requirement Designation 

Quantitative Reasoning (Math & Stat/Logic)









An overview of algebraic number theory, covering factorization and primes, modular arithmetic, quadratic residues, continued fractions, quadratic forms, and diophantine equations.







MATH 4600  Mathematics in Physiology and Medicine












Units: 

4 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 2250 OR MATH 2280.









The goals of the class are (i) to introduce the students to a range of modern mathematical tools; (ii) to teach the students the skill of building tractable mathematical models of biological processes; (iii) to show how to combine the mathematical knowledge, the numerical simulations (in Matlab) and biological intuition to derive new insights into the functioning of living systems. Mathematical topics include introduction to linear algebra, complex numbers, geometric dynamical systems, bifurcation theory, probability, Markov chain, partial differential equations. Biological topics may include modeling heart and circulation, kidneys, circadian clocks, brain rhythms, HIV, antibiotic resistance in bacteria, regulation of gene expression, biological pattern formation.







MATH 4800  Undergraduate Research in Mathematics












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: Instructor Consent.



Honors Course









Explore a topic of significant mathematical interest, or an application of mathematics to a significant problem in science, engineering, or business. Students help to present the material or the results of their own investigations, and write a report on their findings. Prerequisites vary depending on the topic.







MATH 4910  Internship in Mathematics












Units: 

1  4 units




Course Components 










Enrollment Requirement 

Prerequisites: Instructor Consent.









Mathematicsrelated work in industry, business, or government.







MATH 4950  Special Research Projects












Units: 

2  6 units




Course Components 










Enrollment Requirement 

Prerequisites: Instructor Consent.



Honors Course









Projects to be completed as part of the requirements for the Departmental Honors program in mathematics.







MATH 4999  Honors Thesis/Project












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: Instructor Consent.



Honors Course









Restricted to students in the Honors Program working on their University Honors degree.







MATH 5000  Undergraduate Problem Seminar












Units: 

1 units




Course Components 










Enrollment Requirement 

Prerequisites: "B+" or better in MATH 3210 OR Instructor Consent.









Difficult problems presented for solution sharpen skills and develops problemsolving techniques. Prepares students for Putnam Examination (given annually by the Mathematical Association of America).







MATH 5010  Introduction to Probability












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in (MATH 2210 OR MATH 1260 OR MATH 1280 OR MATH 1321 OR MATH 3140).


Requirement Designation 

Quant Reason(Math & Stat/Log) & Quant Intensive BS









Meets with MATH 6805. Combinatorial problems, random variables, distributions, independence and dependence, conditional probability, expected value and moments, law of large numbers, and central limit theorems.







MATH 5030  Actuarial Mathematics












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 5010.


Requirement Designation 

Quantitative Reasoning (Math & Stat/Logic)









Basic introduction to actuarial and insurance mathematics. Helps to prepare students for the third actuarial exam.







MATH 5040  Stochastic Processes and Simulation I












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 5010.


Requirement Designation 

Quant Reason(Math & Stat/Log) & Quant Intensive BS









Meets with MATH 6810. An introductory course in the theory and practice of random processes with special emphasis on problem solving and simulation analysis.







MATH 5050  Stochastic Processes and Simulation II












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 5040.


Requirement Designation 

Quant Reason(Math & Stat/Log) & Quant Intensive BS









Meets with MATH 6815. Second half of the course described under the listing for MATH 5040.







MATH 5075  Time Series Analysis












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 5010.









Meets with MATH 6820. An introduction to the basic topics: difference equations and lag operators, stationary autoregressive moving average processes, forecasting, estimation of parameters, spectral analysis, Kalman filter, introduction to nonlinear time series, processes with deterministic trends, processes with unit roots, cointegration, time series models for heteroskedasticity, and time series with changes in regime.







MATH 5080  Statistical Inference I












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 5010.


Requirement Designation 

Quant Reason(Math & Stat/Log) & Quant Intensive BS









Sampling, sampling distributions, Central Limit Theorem, transformation of data, complete and sufficient statistics, point estimation, optimality.







MATH 5090  Statistical Inference II












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 5080.


Requirement Designation 

Quant Reason(Math & Stat/Log) & Quant Intensive BS









Interval estimation, hypothesis testing, likelihood method, errors, optimality, order statistics, nonparametric methods, rank statistics.







MATH 5110  Mathematical Biology I












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 2280 OR MATH 2250.


Requirement Designation 

Quant Reason(Math & Stat/Log) & Quant Intensive BS









Meets with MATH 6830. Mathematical modeling in the biological and medical sciences. Topics will include continuous and discrete dynamical systems describing interacting and structured populations, resource management, biological control, reaction kinetics, biological oscillators and switches, and the dynamics of infectious diseases.







MATH 5120  Mathematical Biology II












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 5110.


Requirement Designation 

Quant Reason(Math & Stat/Log) & Quant Intensive BS









Meets with MATH 6835. Mathematical models of spatial processes in biology including pattern formation in the embryo and during tissue differentiation, applications of traveling waves to population dynamics, epidemiology, and chemical reactions, and models for neural patterns.







MATH 5140  Foundations of Secondary Mathematics for Teachers I












Units: 

3 units




Course Components 









This is the first course of a threesemester sequence of required courses for students in the MS Mathematics Teaching program. The sequence is designed for students who have a degree in mathematics or a sufficiently strong background in mathematics to explore the main threads of secondary school mathematics from an advanced standpoint.







MATH 5150  Foundations of Secondary Mathematics for Teachers II












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 3100 AND MATH 4030 AND MATH 3070.









This is a second course of a threesemester sequence of required courses for students in the MS Mathematics Teaching program. The sequence is designed for students who have a degree in mathematics or a sufficiently strong background in mathematics to explore the main threads of secondary school mathematics from an advanced standpoint.







MATH 5155  Curriculum and Instruction Practicum I












Units: 

1  2 units




Course Components 









Students will design and present lessons and units associated with mathematics topics developed in the secondary curriculum. This course bridges advanced mathematical topics learned in Math 5150 with their development in secondary schools.







MATH 5160  Foundations of Secondary Mathematics for Teachers III












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 5150.









This is the third course of a threesemester sequence of required courses for students in the MS Mathematics Teaching program. The sequence is designed for students who have a degree in mathematics or a sufficiently strong background in mathematics to explore the main threads of secondary school mathematics from an advanced standpoint.







MATH 5165  Curriculum and Instruction Practicum II












Units: 

2 units




Course Components 









Students will design and present lessons and units associated with mathematics topics developed in the secondary curriculum. This course bridges advanced mathematical topics learned in Math 5150 with their development in secondary schools.







MATH 5210  Introduction to Real Analysis












Units: 

4 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 3220.


Requirement Designation 

Quantitative Reasoning (Math & Stat/Logic)



Honors Course









Metric spaces, fixedpoint theorems and applications, Lebesgue integral, normed linear spaces, approximation, the Fundamental Theorem of Calculus.







MATH 5270  Transformational Geometry












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C+" or better in (MATH 2270 AND MATH 3100).









Students will develop Euclidean geometry through transformational viewpoint. They will consider congruence and similarity using rigid and similarity transformation, then develop matrix theory through the development of linear transformations. They will continue to work on other links between geometry and linear algebra, such as operation on matrices, orthogonality, and so forth.







MATH 5280  Statistics for Teachers












Units: 

3 units




Course Components 









The students in this course will see realworld data sets, understand what makes a data set good or bad for answering the question at hand, appreciate variability, and see quantification and explanation of variability via statistical models. This course will center around statistical concepts and realworld case studies, and will make use of technology in an active learning environment. The topics covered are: formulation of statistical questions, exploration and display of univariate (bivariate) data sets; bivariate measurement data (scatter plots, association, simple linear regression, correlation); introduction to the use of randomization and simulation in data production and inferential reasoning; and introduction to probability from a relative frequency perspective, including additive and multiplicative rules, conditional probability an independence.







MATH 5310  Introduction to Modern Algebra I












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 3210 AND (MATH 3220 OR MATH 4400 OR MATH 4510).


Requirement Designation 

Quantitative Reasoning (Math & Stat/Logic)









An introduction to groups, rings, and fields.







MATH 5320  Introduction to Modern Algebra II












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 5310.


Requirement Designation 

Quantitative Reasoning (Math & Stat/Logic)









Second half of the course described under the listing for MATH 5310.







MATH 5405  Cryptography, Codes, and Computational Number Theory












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 4400.









Classic and modern methods of encryption, applications to publickey ciphers (RSA, El Gamnal, etc.), random number generators, attacks on encryption systems, error correcting codes; computational number theory. A project/paper will be required.







MATH 5410  Introduction to Ordinary Differential Equations












Units: 

4 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in (MATH 2250 OR MATH 2280).


Requirement Designation 

Quant Reason(Math & Stat/Log) & Quant Intensive BS









Meets with MATH 6840. Linear ordinary differential equations: initialvalue problems and behavior of solutions. Nonlinear equations: existence, uniqueness, perturbations, extension to the boundary. Introduction to dynamical systems and their relation to differential equations.







MATH 5420  Ordinary Differential Equations and Dynamical Systems












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 5410.


Requirement Designation 

Quant Reason(Math & Stat/Log) & Quant Intensive BS









Meets with MATH 6845. Continuation of the study of dynamical systems, through a discussion of stability and its absence, concrete examples. SturmLiouville theory, including the existence of complete orthormal systems of eigenfunctions.







MATH 5440  Introduction to Partial Differential Equations












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in (MATH 2280 OR MATH 3140 OR MATH 3150).


Requirement Designation 

Quant Reason(Math & Stat/Log) & Quant Intensive BS









Meets with MATH 6850. Classical wave, Laplace, and heat equations. Fourier analysis, Green's functions. Methods of characteristics. MATH 3210 (Foundations of Analysis I) is recommended but not necessary for this class.







MATH 5470  Chaos and Nonlinear Systems












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 2280 OR MATH 2250.


Requirement Designation 

Quantitative Reasoning (Math & Stat/Logic)









Meets with MATH 6440. Introduction to chaotic motions, strange attractors, fractal geometry. Models from fluid dynamics and mechanical and electrical oscillators.







MATH 5500  Calculus of Variations with Applications












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in (MATH 2280 OR (MATH 2250 AND (MATH 3150 OR MATH 3140))).









Introduces the Calculus of Variations and gives an introduction to a range of applications in physics, mechanics, signal processing, and some topics of geometry.







MATH 5510  Introduction to Algebraic and Geometric Topology I












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 3220.


Requirement Designation 

Quantitative Reasoning (Math & Stat/Logic)









Introduction to metric spaces, Lipschitz maps, isometries, group of isometries of the Euclidean plane, surfaces as metric spaces, geodesics, topological spaces, continuity, compactness, connectedness, identification spaces.







MATH 5520  Introduction to Algebraic and Geometric Topology II












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 5510.


Requirement Designation 

Quant Reason(Math & Stat/Log) & Quant Intensive BS









Surfaces, their topological classification, introduction to algebraic topology through the fundamental group, covering spaces, geometry of the universal covering spaces of surfaces (Euclidean, spherical, hyperbolc), GaussBonnet theorem.







MATH 5600  Survey of Numerical Analysis












Units: 

4 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in ((MATH 2210 OR MATH 1260 OR MATH 1280 OR MATH 1321 OR MATH 3140) AND (MATH 2270 OR MATH 2250)).


Requirement Designation 

Quant Reason(Math & Stat/Log) & Quant Intensive BS









Meets with MATH 6855. Numerical linear algebra, interpolation, integration, differentiation, approximation (including discrete and continuous least squares, Fourier analysis, and wavelets), initial and boundaryvalue problems of ordinary and partial differential equations. Programming experience is necessary prior to taking this course.







MATH 5610  Introduction to Numerical Analysis I












Units: 

4 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in ((MATH 2210 OR MATH 1260 OR MATH 1280 OR MATH 1321 OR MATH 3140) AND (MATH 2270 OR MATH 2250)).


Requirement Designation 

Quant Reason(Math & Stat/Log) & Quant Intensive BS









Meets with MATH 6860. Numerical linear algebra, interpolation, integration, differentiation, approximation (including discrete and continuous least squares, Fourier analysis, and wavelets). Programming experience is necessary prior to taking this course.







MATH 5620  Introduction to Numerical Analysis II












Units: 

4 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 5610.


Requirement Designation 

Quant Reason(Math & Stat/Log) & Quant Intensive BS









Meets with MATH 6865. Numerical solution of initial and boundary value problems of ordinary and partial differential equations.







MATH 5700  Capstone Course in Mathematics












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 4030 AND MATH 3100.









The Capstone Course in Mathematics examines secondary school mathematics from an advanced point of view. The topics covered are drawn from Abstract Algebra, Analysis, and Geometry and are rooted in the core secondary curriculum of number and operations, algebra, geometry, and functions. Students learn to generalize definitions and theorems that help to unite and explain mathematics. As they explore familiar secondary mathematic problems from a higher perspective, they draw connections between ideas taught separately in different courses. Through their work in the course, they improve their ability to promote their students' understanding of mathematics and to make better decisions regarding the direction of their lessons and curriculum.







MATH 5710  Introduction to Applied Mathematics I












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in (MATH 2250 AND MATH 3150) OR (MATH 2280 AND MATH 2270) OR MATH 3140.


Requirement Designation 

Quant Reason(Math & Stat/Log) & Quant Intensive BS









Symmetric linear systems, positive definite matrices, eigenvalue problems, equilibrium equations for discrete and continuous systems, boundary value problems in ODEs and PDEs, boundary integrals.







MATH 5740  Mathematical Modeling












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in (MATH 2250 OR (MATH 2270 AND MATH 2280)).


Requirement Designation 

Quant Reason(Math & Stat/Log) & Quant Intensive BS









Meets with MATH 6870. Development of mathematical models for physical, biological, engineering, and industrial phenomena and problems, and their solution using a wide variety of tools. Taught through case studies.







MATH 5750  Topics in Applied Mathematics












Units: 

3 units




Course Components 










Enrollment Requirement 

Instructor's Consent.


Requirement Designation 

Quant Reason(Math & Stat/Log) & Quant Intensive BS









Meets with MATH 6880. Consult Math Department for specific offering. Possible topics include integral equations, calculus of variations, control theory, continuum mechanics, applied matrix theory, vector and tensor analysis, applications of probability and statistics. Will be offered occasionally on the basis of need or interest.







MATH 5760  Introduction to Mathematical Finance I












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 5010 AND MATH 2280.









Meets with MATH 6890. A basic introduction to the theory of financial derivative pricing. Topics include no arbitrage principle, riskneutral measure, BlackScholes theory, numerical model implementation and parameter calibration.







MATH 5765  Introduction to Mathematical Finance II












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 5760.









Meets with MATH 6895. Continuoustime finance fundamentals, topics include exotic options, interest rate term structure models, jump processes, credit models, and statistical arbitrage strategies.







MATH 5770  Introduction to Optimization












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 2250 OR MATH 2270 OR instructor consent.









Meet with MATH 6640. Existence, uniqueness and characterization of solutions to finite dimensional unconstrained and constrained optimization problems. Solution methods for finite dimensional unconstrained and constrained optimization problems. Newton and QuasiNewton methods. Globalization strategies. Linear Programming. Least Squares. Quadratic Programming. Convex Programming. Some programming experience is recommended. For graduate students extra work is required.







MATH 5900  Topics in Mathematics












Units: 

1  4 units




Course Components 










Enrollment Requirement 

Prerequisites: Instructor Consent.









Various topics in mathematics to be treated at the appropriate level.







MATH 5910  Supervised Reading












Units: 

1  6 units




Course Components 










Enrollment Requirement 

Prerequisites: Instructor Consent.


Requirement Designation 

Quantitative Reasoning (Math & Stat/Logic)







MATH 5960  Undergraduate Special Projects












Units: 

4 units




Course Components 










Enrollment Requirement 

Prerequisites: Instructor Consent.


Requirement Designation 

Quantitative Reasoning (Math & Stat/Logic)









Special computer project to serve as a senior thesis for students in scientificcomputing emphasis.







MATH 5969  Special Topics in Statistics












Units: 

1  6 units




Course Components 










Enrollment Requirement 

Prerequisites: Instructor Consent.









Topics vary. Taught by members of the University Statistics Committee. Check current class schedule for crosslistings.







MATH 6010  Linear Models












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 5010 AND MATH 5080 AND MATH 5090 AND MATH 2270.









Univariate linear models with applications to regression and ANOVA.







MATH 6020  Multilinear Models












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 6010.









Multivariate linear models with applications to regression and ANOVA.







MATH 6040  Mathematical Probability












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 6210.









Analytical approach to probability theory, random variables and their distributions, limit theorems for sums of independent random variables.







MATH 6070  Mathematical Statistics












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 2270 AND MATH 5080.









Topics from distribution theory, estimation, and hypothesis testing.







MATH 6080  Topics in Contemporary Mathematics












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: Graduate Status.









This course is intended to broaden student's perspective of mathematical research areas, while simultaneously introducing important mathematical concepts. More than a survey course, each instructor will spend 46 weeks discussing a topic of contemporary mathematics in depth, and there will be two to three such modules in the course. The idea is to start from the beginning, developing the selected topic to the point that students can grasp some of the central ideas important at a research level. Students will be required to choose one of the topics from which they will be assigned to read two research papers, write a survey paper and present their topic to the peers and the faculty member from that field.







MATH 6090  Advanced Topics in the History of Mathematics












Units: 

3 units




Course Components 









This course is part of the curriculum specific to the emphasis in Mathematics Teaching. Each semester, one or two particular topics are discussed from a historical perspective, tracing the demise of failed interpretations as well as the development of the current understanding. Illuminating the difficulties associated with understanding a topic by examining wrong turns deepens understanding.







MATH 6100  Conceptual Calculus for Mathematics Teachers












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: MATH 5150 AND MATH 5160.









In this course the students will develop conceptual understanding of calculus as it is needed for successful teaching of secondary curriculum. The students will learn how the ideas of calculus are rooted in other topics encountered in middle and high school. The topics covered will include concepts of differential and integral calculus, computations of derivatives and integrals as well as their applications.







MATH 6130  Introduction to Algebraic Geometry I












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 6310 AND MATH 6320.









Affine and projective varieties, tangent spaces and singularities, curve theory.







MATH 6140  Introduction to Algebraic Geometry II












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 6130.









Surfaces, intersection theory, special varieties, introduction to schemes.







MATH 6150  Complex Manifolds












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 6220.









Material will be selected from Riemann surfaces and algebraic curves, Kaehler geometry, Stein manifold theory, compact surfaces, etc.







MATH 6160  Complex Algebraic Curves












Units: 

3 units




Course Components 









The Riemann sphere and elliptic curves, plane curves, their intersection multiplicities and Bezout's theorem, Divisors and linear series on Riemann surfaces, the canonical line bundle, the RiemannHurwitz and RiemannRoch theorems, Jacobians and Abel's Theorem, special linear series, Clifford's Theorem, introduction to moduli.







MATH 6170  Introduction to Riemannian Geometry












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 6510.









Riemannian metrics, connections, geodesics, normal coordinates, completeness, spaces of constant curvature, submanifolds, Bonnet's and Meyer's theorem, CartanHadamard theorem, Alexandrov and Topogonov comparison theorems, closed geodesics, cut locus, sphere theorem.







MATH 6180  Topics in Complex Geometry












Units: 

3 units




Course Components 









This course is meant for second or third year PhD students who have completed their preliminary exams in Algebra and Geometry. Topics will vary but may include an introduction to algebraic surfaces over the complex numbers, or an introduction to Hodge theory.







MATH 6210  Real Analysis












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 5210.









Measures and integrals, Lpspaces, Hilbert spaces, Banach spaces, Fourier series.







MATH 6220  Complex Analysis












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 4200 AND MATH 6210.









Analytic functions, complex integration, conformal mapping, families of analytic functions, zeros of analytic functions, analytic continuation.







MATH 6240  Lie Groups/Lie Algebras I












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 6220.









Basic theory of Lie groups and Lie algebras.







MATH 6250  Lie Groups/Lie Algebras II












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 6240.









Structure theory, classification, and finite dimensional representations of Lie groups. Compact Lie groups.







MATH 6260  Representation Theory












Units: 

3 units




Course Components 









This course is an introduction to representation theory of topological groups. it is meant for second or third year PhD students who have completed their preliminary exams in Analysis and Algebra, and does not assume knowledge of Lie group theory. This course extends ideas from the representation theory of finite groups to the setting of topological groups. The main topic of the study is the representation theory of compact groups, in particular compact matrix groups.







MATH 6310  Modern Algebra I












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 5320.









Groups, rings, modules, homological algebra, fields, and Galois theory.







MATH 6320  Modern Algebra II












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 6310.









Second half of the course described under the listing for MATH 6310.







MATH 6350  Commutative Algebra












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 6320.









Various topics in commutative algebra. The course will be offered on the basis of need or interest. May be repeated for credit when the topics vary.







MATH 6370  Algebraic Number Theory












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 6320.









This is a dedicated course for graduate students in number theory. List of Topics: Dedekind domains. Extension. Class group units: Minkowski's reduction theory and Dirichlet's unit theorem. Lfunctions. Cyclotomic fields. Statement of Artin Reciprocity Law.







MATH 6410  Ordinary Differential Equations












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 5210.









Existence, uniqueness theory; stability theory; invariant sets and manifolds; periodic motions; bifurcation theory; boundary value problems; applications.







MATH 6420  Partial Differential Equations












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 5210.









Firstorder equations: characteristics, transport equations, shocks, HamiltonJacobi theory. Boundary value problems for the Laplace equation: maximum principles, Green's functions, Hilbert space methods. Cauchy and initialboundary value problems for the heat equation and wave equation: existence and basic properties.







MATH 6430  Advanced Partial Differential Equations












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 6420.









Advanced topics from among the following: systems of conservations laws, nonlinear elliptic and parabolic equations, viscosity solutions of evolution problems, free boundary problems, applications.







MATH 6440  Advanced Dynamical Systems












Units: 

3 units




Course Components 









Meets with MATH 5470. Basic abstract dynamics; stable, unstable, center manifold theory; index theories; KAM theory; chaos; dimensions of attractors; forced oscillations; applications.







MATH 6510  Differentiable Manifolds












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 4510 AND MATH 5520.









Manifolds, tangent spaces, orientation, Whitney's embedding theorem, transversality, Sard's theorem, partitions of unity, tubular neighborhoods, fiber bundles, degree theory, vector fields, flows, Lie derivatives, Frobenius' integrability theorem, differential forms, DeRham cohomology.







MATH 6520  Introduction to Algebraic Topology












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 5520 AND MATH 6510.









Simplicial and cell complexes, homology and cohomology with coefficients, excision, MayerVietoris sequence, cup and cap products, DeRham theorem, Euler characteristic, PoincareHopf theorem, higher homotopy groups, long exact sequence of a fiber bundle, elementary homotopy theory.







MATH 6610  Analysis of Numerical Methods I












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 5620.









Mathematical analysis of numerical methods in linear algebra, interpolation, integration, differentiation, approximation (including least squares, Fourier analysis, and wavelets), initial and boundaryvalue problems of ordinary and partial differential equations.







MATH 6620  Analysis of Numerical Methods II












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 6610.









Second half of the course described under the listing for MATH 6610.







MATH 6630  Numerical Solutions of Partial Differential Equations












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 6610 AND MATH 6620 AND MATH 6420.









Analysis and implementation of numerical methods for solving partial differential equations. Issues of stability and accuracy. Linear and nonlinear problems.







MATH 6640  Introduction to Optimization












Units: 

3 units




Course Components 









Meets with MATH 5570. Existence, uniqueness and characterization of solutions to finite dimensional unconstrained and constrained optimization problems. Solution methods for finite dimensional unconstrained and constrained optimization problems. Newton and quasiNewton methods. Globalization strategies, Linear Programming. Least Squares. Quadratic Programming. Convex Programming. Some programming experience is recommended. For graduate students extra work is required.







MATH 6710  Applied Linear Operator and Spectral Methods












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 5210 AND MATH 5410.









The theory of linear operators applied to matrix, differential and integral equations, the Fredholm alternative, spectral theory, inverse and pseudoinverse operators, HilbertSchmidt theory and eigenfunction expansions.







MATH 6720  Applied Complex Variables and Asymptotic Methods












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 5210 AND MATH 5410.









CauchyRiemann equations, Cauchy integral formulas, Taylor and Laurent series, multivalued functions, branch points and cuts, analytic continuation, Jordan's lemma, evaluation of real integrals; potential theory, stream functions, conformal mapping, special functions, Fourier, Laplace, Hilbert, and Z transforms, scattering theory, asymptopic analysis of integrals, Laplace's method, Watson's lemma, method of steepest descents.







MATH 6730  Asymptotic and Perturbation Methods












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 6720.









Asymptotic analysis, initialvalue problems, multiscale analysis and the averaging theorem, homogenization theory, boundary and transitionlayer problems, matched asymptotic expansions, relaxation oscillations and propagating transition layers. Applications to problems from the physical and life sciences.







MATH 6740  Bifurcation Theory












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 6210 AND MATH 6220.









Degree theories; method of Liapunov and Schmidt; local and global bifurcation theory; Hopf bifurcation; LiusternikShnirelman theory; applications.







MATH 6750  Fluid Dynamics












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or bette rin MATH 5440 OR MATH 6420.









Derivation of equations of fluid dynamics, Euler and NavierStokes equations, Bernoulli's theorem, Kelvin's circulation theorem, potential flow, exact solutions, hydrodynamic paradoxes, vorticity, compressibility, thermal convection, waves in fluids, fluid instabilities, turbulence.







MATH 6760  Continuum Mechanics: Solids












Units: 

3 units




Course Components 









Linear and nonlinear elasticity theory, transport phenomena, electromagnetic and elastic wave propogation and variational principles. Additional possible topics include piezoelectricity, thermoelectricity, viscoelasticity, magnetic materials, the Hall effect, quasiconvexity and phase transitions, shape memory and composite materials.







MATH 6770  Mathematical Biology I












Units: 

3 units




Course Components 









Topics will alternate between (a) ecology and population biology and (b) physiology and cell biology.







MATH 6780  Mathematical Biology II












Units: 

3 units




Course Components 









Second half of the course described under the listing for MATH 6770, of which it is the continuation.







MATH 6790  Case Studies in Computational Engineering and Science












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 5740.









Two to five faculty members from various disciplines will describe in detail a project in which they are engaged that involves all ingredients of computational engineering and science: a scientific or engineering problem, a mathematical problem leading to mathematical questions, and the solution and interpretation of these questions obtained by the use of modern computing techniques. Participating faculty will vary from year to year. To be offered on the basis of need.







MATH 6795  Seminar in Computational Engineering and Science












Units: 

1  5 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 6790.









Students in the final semester of the Computational Engineering and Science Program will present their own CESrelated research. To be offered on the basis of need.







MATH 6805  Introduction to Probability












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 2210.









Meets with MATH 5010. For Ph.D. students only. Extra work is required; this should be arranged with the instructor before the end of the second week of classes.







MATH 6810  Stochastic Processes and Simulation I












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 5010.









Meets with MATH 5040. For Ph.D. students only. Extra work is required; this should be arranged with the instructor before the end of the second week of classes.







MATH 6815  Stochastic Processes and Simulation II












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 5010 AND MATH 5040.









Meets with MATH 5050. For Ph.D. students only. Extra work is required; this should be arranged with the instructor before the end of the second week of classes.







MATH 6820  Time Series Analysis












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 5010.









Meets with MATH 5075. For Ph.D. students only. Extra work is required; this should be arranged with the instructor before the end of the second week of classes.







MATH 6824  Statistical Inference I












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: MATH 5010 OR MATH 6805.









Meets with MATH 5080. For PhD students only. Extra work is required, including statistical projects, based on material covered, using software.







MATH 6828  Statistical Inference II












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: MATH 5080 OR MATH 6824.









Meets with MATH 5090. For PhD students only. Extra work is required, including statistical projects, based on material covered, using software.







MATH 6830  Mathematical Biology I












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 2280 OR MATH 3150 OR Instructor Consent.









Meets with MATH 5110. For Ph.D. students only. Extra work is required; this should be arranged with the instructor before the end of the second week of classes.







MATH 6835  Mathematical Biology II












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 5110.









Meets with MATH 5120. For Ph.D. students only. Extra work is required; this should be arranged with the instructor before the end of the second week of classes.







MATH 6840  Introduction to Ordinary Differential












Units: 

4 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 3220.









Meets with MATH 5410. For Ph.D. students only. Extra work is required; this should be arranged with the instructor before the end of the second week of classes.







MATH 6845  Ordinary Differential Equations and Dynamical Systems












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 5410 OR Instructor Consent.









Meets with MATH 5420. For Ph.D. students only. Extra work is required; this should be arranged with the instructor before the end of the second week of classes.







MATH 6850  Introduction to Partial Differential Equations












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 3220.









Meets with MATH 5440. For Ph.D. students only. Extra work is required; this should be arranged with the instructor before the end of the second week of classes.







MATH 6855  Survey of Numerical Analysis












Units: 

4 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 2210 AND MATH 2250 AND MATH 2280.









Meets with MATH 5600. For Ph.D. students only. Extra work is required; this should be arranged with the instructor before the end of the second week of classes.







MATH 6860  Introduction to Numerical Analysis I












Units: 

4 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 2210 AND (MATH 2250 OR MATH 2270) AND MATH 2280 AND Computing Experience.









Meets with MATH 5610. For Ph.D. students only. Extra work is required; this should be arranged with the instructor before the end of the second week of classes.







MATH 6865  Introduction to Numerical Analysis II












Units: 

4 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 5610.









Meets with MATH 5620. For Ph.D. students only. Extra work is required; this should be arranged with the instructor before the end of the second week of classes.







MATH 6870  Mathematical Model












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 5600 OR CS 5220.









Meets with MATH 5740. For Ph.D. students only. Extra work is required; this should be arranged with the instructor before the end of the second week of classes. Development of mathematical models for physical biological, engineering, industrial and societal phenomena and problems, and their solution using a wide variety of tools. Taught through case studies.







MATH 6875  Methods of Optimization












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 3150.









Meets with MATH 5450. For Ph.D. students only. Extra work is required; this should be arranged with the instructor before the end of the second week of classes.







MATH 6880  Topics in Applied Mathematics












Units: 

3 units




Course Components 









Meets with MATH 5750. For Ph.D. students only. Extra work is required; this should be arranged with the instructor before the end of the second week of classes.







MATH 6890  Introduction to Mathematical Finance I












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 2280 AND MATH 5010.









Meets with MATH 5760. For Ph.D. students only. Extra work is required; this should be arranged with the instructor before the end of the second week of classes.







MATH 6895  Introduction to Mathematical Finance II












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 2280 AND MATH 5010.









Meets with MATH 5765. For Ph.D. students only. Extra work is required; this should be arranged with the instructor before the end of the second week of classes. Continuoustime finance fundamentals, topics include exotic options, interest rate term structure models, jump processes, credit models, and statistical arbitrage strategies.







MATH 6910  Supervised Reading












Units: 

1  6 units




Course Components 







MATH 6920  Topics in Analysis












Units: 

3 units




Course Components 









Various topics in analysis such as functional analysis, harmonic analysis and dynamics offered on the basis of need or interest.







MATH 6950  Topics in Algebraic Topology












Units: 

3 units




Course Components 









This is an advanced course in algebraic topology. Topics will vary but may include characteristic classes, rational homotopy theory and Morse theory.







MATH 6960  Special Projects












Units: 

1  6 units




Course Components 







MATH 6970  Thesis Research: Master's












Units: 

1  9 units




Course Components 







MATH 6980  Faculty Consultation












Units: 

3 units




Course Components 









Usually only one sequence from each decade (e.g., 711 to 719) is offered in any year.







MATH 7280  Operator Theory












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: "C" or better in MATH 6210 AND MATH 6220.









A study of linear operators, primarily in Hilbert spaces.







MATH 7310  Various Topics in Algebra












Units: 

3 units




Course Components 










Enrollment Requirement 

Prerequisites: Instructor Consent.









This graduate course will be offered on the basis of need or interest, covering various topics in algebra. The material will vary according to instructor and student interest, with possible topics being noncommutative geometry, Weyl algebras and Dmodules, cluster algebras, etc.







MATH 7710  Optimization












Units: 

3 units




Course Components 









Discusses modern problems in calculus of variations and optimal control, especially in the structural optimizations, as well as the foundations of these disciplines. Offered on the basis of need or interest.







MATH 7800  Topics in Algebraic Geometry












Units: 

3 units




Course Components 









Various topics in the area of algebraic geometry, offered on the basis of need or interest.







MATH 7810  Topics in Riemannian Geometry












Units: 

1  3 units




Course Components 









Various topics in the area of Riemannian geometry, offered on the basis of need or interest.







MATH 7815  Seminar in Differential Geometry












Units: 

1  3 units




Course Components 







MATH 7825  Seminar in Analysis












Units: 

1  3 units




Course Components 







MATH 7830  Topics in Commutative Algebra












Units: 

3 units




Course Components 









Various topics in the area of commutative algebra, offered on the basis of need or interest.







MATH 7835  Seminar in Algebra












Units: 

1  3 units




Course Components 







MATH 7845  Seminar in Differential Equations





