#### MAT-101 *Survey of Algebra and Probability*1
credit

**Prerequisites:**Placement according to the Math Placement Guide

Students in this course develop fundamental arithmetic and algebra skills in preparation for MAT-125. Topics will include Cartesian coordinates and graphs, linear models, and algebraic expressions. This course also includes topics in probability, including calculating experimental and theoretical probabilities.

#### MAT-102 *Functions*1
credit

**Prerequisites:**MAT-101 or placement according to the Math Placement Guide.

In preparation for MAT-150, students in this course acquire foundational understanding of the formulation and interpretation of functions, which model relationships among quantities. Examples from the course include linear, quadratic, radical, exponential, and logarithmic models. Students master function notation, basic transformations, variables and parameters, and domain and range, and apply these ideas to analyze functions graphically, numerically, and symbolically, and to solve equations, including systems of two linear equations.

#### MAT-111 *Contemporary Mathematics*3
credits

**Prerequisites:**MAT-101 or placement according to the Math Placement Guide.

A course designed to explore some of the great ideas in mathematics and to discover the power of mathematical thinking in everyday life. Topics include counting techniques, infinity, geometry, shape and space, chaos and fractals, and decision science.

#### MAT-125 *Data Analysis and Statistics*3
credits

**Prerequisites:**MAT-101 or placement according to the Math Placement Guide.

An applications-oriented approach to data analysis and statistics. Topics may include descriptive statistics, probability and probability distributions, confidence intervals, hypothesis testing, and regression. The course will also cover linear inequalities and interpreting functions with emphasis on their graphs. Applications in business, economics, natural sciences, and the social sciences. Students who have received credit for AP Statistics may not take this course for credit.

#### MAT-130 *Trigonometry*1
credit

**Prerequisites:**MAT-102, MAT-150, or placement according to the Math Placement Guide.

Students in this course acquire knowledge of trigonometry in preparation for MAT-175. The course includes topics in right triangle trigonometry, such as measurement of angles, evaluation of trigonometric functions, sketching and analysis of graphs of trigonometric functions, inverse trigonometric functions, solution of trigonometric equations, the Pythagorean theorem, and other trigonometric identities.

#### MAT-150 *Applied Calculus: A Modeling Approach*4
credits

**Prerequisites:**MAT-102 or placement according to the Math placement guide.

An introductory course in differential and integral calculus, useful for work in the natural sciences and the social sciences, with a strong emphasis on developing scientific computing and mathematical modeling skills. Topics may include functions of one or more variables, differentiation, integration, and applications, including an early exposure to differential equations and initial value problems, some introductory vector analysis and linear algebra, and techniques of estimation. This course is designed to be suitable both for students with no prior experience of calculus and for students with some AP calculus experience.

#### MAT-175 *Single Variable Calculus*4
credits

**Prerequisites:**MAT-150 with a B- or better, or MAT-150 and MAT-130, each with a grade of C or better, or placement according to the Math placement guide.

This calculus course studies the theory of differentiation and integration of functions of one variable. Main topics include functions, limits, differentiation, and integration. Topics may include continuity, Riemann sums, the fundamental theorem of calculus, techniques of integration, improper integrals, l'Hopital's rule, geometric series, power series, and Taylor series. This is a more mathematically rigorous course than MAT-150. Students planning further work in mathematics or physics and who have successfully completed a previous calculus course are encouraged to take MAT-175.

#### MAT-199 *Math and Physics Colloquium*.5
credits

A series of talks on topics related to mathematics and the physical sciences, intended to expose students to opportunities available in these fields. Topics may include current research projects, summer internship reports, and career development. May be repeated for credit.

#### MAT-212 *Multiple Regression Analysis*3
credits

**Prerequisites:**MAT-125, MAT-150, MAT-175, MAT-275, or equivalent course with a minimum grade of C.

Introduction to statistical methods for a mathematics or science major. Topics include include analysis of variance, multiple regression and analysis, chi square, and time series. A statistical software package will be used. Students who have taken calculus should take this course rather than MAT-125.

#### MAT-221 *Mathematics for Elementary Teachers I*4
credits

**Prerequisites:**MAT-102 or placment according to the Math Placement Guide.

Topics include number systems, problem solving, sets, logic and properties of whole numbers and rational numbers. The emphasis is on mathematics taught in the elementary school classroom, using a variety of teaching techniques, methods, and hands-on materials including manipulatives and technology.

#### MAT-222 *Mathematics for Elementary Teachers II*4
credits

**Prerequisites:**MAT-102 or placement according to the Math Placement Guide.

Topics include properties of real numbers, descriptive statistics and geometry. The emphasis is on mathematics taught in the elementary school classroom, using a variety of teaching techniques, methods, and hands-on materials including manipulatives and technology.

#### MAT-252 *Discrete Mathematics*3
credits

**Prerequisites:**MAT-280, MAT-281, MAT-282, or MAT-283 with a minimum grade of C.

Systems of linear equations, matrix operations, combinatorics, graph theory. Offered Spring term of odd numbered years.

#### MAT-275 *Multivariable Calculus*4
credits

**Prerequisites:**MAT-175 with minimum grade of C, or meet the criteria of the Math placement guide, or Instructor permission.

This course is an extension of calculus to higher-dimensional spaces. Main topics include differentiation of functions of two and three variables, an introduction to vector analysis and parameterization, and a study of definite integration in both rectangular and curved coordinate systems. Topics may include a review of functions of several variables, vector geometry of 3-dimensional space, partial derivatives, gradient vectors, optimization techniques, multiple integration in the three classical curvilinear coordinate systems, parametric equations, vector fields, line integrals and Green's Theorem, and the other classical integral theorems of differential geometry.

#### MAT-280 *Introduction to Proof: Number Theory*1
credit

**Prerequisites:**MAT-175 or MAT-275 with a minimum grade of C and Sophomore standing or Instructor permission.

Methods of mathematical proof will be introduced using concepts from number theory. Topics may include: axioms for the integers, Euclidean algorithm, Diophantine equations, Fermat's Little Theorem, unique factorization, and primality testing.

#### MAT-281 *Introduction to Proof: Combinatorics*1
credit

**Prerequisites:**MAT-175 or MAT-275 with a minimum grade of C and Sophomore standing or Instructor permission.

Methods of mathematical proof will be introduced using concepts from combinatorics. Topics may include: permutations and combinations, finite mathematical structures, inclusion-exclusion principle, and elements of the theory of graphs.

#### MAT-282 *Introduction to Proof: Sets and Functions*1
credit

**Prerequisites:**MAT-175 or MAT-275 with a minimum grade of C and Sophomore standing or Instructor permission.

Methods of mathematical proof will be introduced using concepts from sets and functions. Topics may include: the basics of set theory including equivalence relations, cardinality (including the notions of countability and uncountability), and topics covering surjective, injective, bijective, and inverse functions.

#### MAT-283 *Introduction to Proof: Logic*1
credit

**Prerequisites:**MAT-175 or MAT-275 with a minimum grade of C and Sophomore standing or Instructor permission.

Methods of mathematical proof will be introduced using concepts from symbolic logic. Topics may include: an introduction to logical implication, quantifiers, contrapositive, and logical equivalence.

#### MAT-294 *Independent Study*1
- 3
credits

**Prerequisites:**Instructor permission

Independent study of selected areas of mathematics not available in the regular curriculum. See independent study guidelines.

#### MAT-311 *Probability and Mathematical Statistics I*3
credits

**Prerequisites:**MAT-280, MAT-281, MAT-282, or MAT-283 with a minimum grade of C.

A study of finite sample spaces, conditional probability and independence, functions of random variables, random variables of one or more dimensions, discrete random variables, continuous random variables, moment generating functions, sampling distribution, estimation and testing of hypotheses.

#### MAT-312 *Probability and Mathematical Statistics II*3
credits

**Prerequisites:**MAT-311 with a minimum grade of C.

A continuation of MAT-311. A study of finite sample spaces, conditional probability and independence, functions of random variables, random variables of one or more dimensions, discrete random variables, continuous random variables, moment generating functions, sampling distribution, estimation and testing of hypotheses.

#### MAT-352 *Differential Equations*3
credits

**Prerequisites:**MAT-275 or equivalent course with a minimum grade of C.

A study of the solution and applications of ordinary differential equations including systems of equations using matrix algebra.

#### MAT-361 *Linear Algebra*3
credits

**Prerequisites:**MAT-280, MAT-281, MAT-282, or MAT-283 with a minimum grade of C.

A study of general vector spaces, linear transformations, eigenvalues and eigenvectors.

#### MAT-370 *Geometry*3
credits

**Prerequisites:**MAT-280, MAT-281, MAT-282, or MAT-283 with a minimum grade of C.

A study of Euclidean geometry and the development of non-Euclidean geometry, one of the most significant occurrences in the history of mathematics.

#### MAT-372 *History of Mathematics*3
credits

**Prerequisites:**MAT-280, MAT-281, MAT-282, or MAT-283 with a minimum grade of C.

A historical survey of the ideas, tools, and symbols of mathematics and the people who developed them. For upper-division students who are planning to teach or otherwise pursue mathematics as a profession.

#### MAT-431 *Complex Analysis*3
credits

**Prerequisites:**MAT-280, MAT-281, MAT-282, or MAT-283 with a minimum grade of C.

A study of complex-valued analytic functions. Topics may include Cauchy's theorem, Laurent series, integration, the residue theorem, and conformal mapping.

#### MAT-441 *Topology*3
credits

**Prerequisites:**MAT-280, MAT-281, MAT-282, or MAT-283 with a minimum grade of C.

An introduction to the techniques and theorems of point-set topology and metric spaces. Topics include: cardinality, separation axioms, compactness, connectedness, continuity and finite products.

#### MAT-451 *Real Analysis*3
credits

**Prerequisites:**MAT-280, MAT-281, MAT-282, or MAT-283 with a minimum grade of C.

A study of the basic concepts of real analysis. Topics include limits, sequences, series, continuity, differentiation, and integration.

#### MAT-461 *Abstract Algebra*3
credits

**Prerequisites:**MAT-280, MAT-281, MAT-282, or MAT-283 with a minimum grade of C.

An introduction to the study of abstract algebra via the theory of groups and rings.

#### MAT-494 *Independent Study*1
- 3
credits

**Prerequisites:**Instructor permission

Research studies for qualified mathematics majors. See independent study guidelines See independent study guidelines.

#### MAT-497 *Internship*1
- 3
credits

**Prerequisites:**Instructor permission

Individually arranged programs of work and study with the department, academic institutions, private industries, or government agencies.

#### MAT-498 *Upper-Division Seminar*1
- 3
credits

**Prerequisites:**Junior or Senior standing with major in mathematics.

Study of topics in mathematics not covered in previous mathematics courses. May be repeated for credit.