## Mathematics and Physical Sciences - Mathematics (MAT) Courses

#### MAT-105 *Algebra*
3 credits

**Prerequisites: **High school Algebra 2 or equivalent or placement.

Intensive study of algebra, graphs and functions. The emphasis will be on gaining college level proficiency in algebra and understanding the graphs and properties of functions. Topics include linear, quadratic, radical, rational, exponential and logarithmic functions. Intended to prepare students for MAT-111, MAT-112, MAT-123.1, and MAT-149.

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

**Prerequisites: **MAT-105 or equivalent.

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-112 *Introduction to Statistics*
3 credits

**Prerequisites: **MAT-105 or equivalent.

An applications-oriented approach to the use of statistics. Topics covered include descriptive statistics, frequency distributions, mean, standard deviations, probability and probability distributions, inferential statistics, confidence intervals and hypothesis testing and bivariate statistics.

#### MAT-123.1 *Applied Mathematics*
3 credits

**Prerequisites: **MAT-105 or equivalent.

An applications-oriented course to review algebra. Subjects include solving equations, inequalities, functions, graphs, logarithms, exponentials and probability. Applications in business, economics and the social sciences.

#### MAT-124.1 *Applied Calculus*
3 credits

A continuation of MAT-123 introducing both differential and integral calculus. Examples drawn from business, economics, biology, and the social and behavioral sciences.

#### MAT-149 *Pre-Calculus*
4 credits

**Prerequisites: **MAT 105 or one year of high school mathematics beyond geometry and Algebra 2 or equivalent.

Topics in algebra and trigonometry beyond those covered in the second course in high school algebra. Emphasis is placed on concepts, structures and technical competence. Topics include solutions of algebraic equations and inequalities; functions and graphs; exponential, logarithmic, and trigonometric functions; elementary plane analytic geometry.

#### MAT-151 *Calculus I*
4 credits

**Prerequisites: **MAT 149 or equivalent.

A study of differential and integral calculus of real functions of one real variable. Topics include limits and continuity, differentiation, the chain rule, the mean-value theorem, the fundamental theorem of calculus, curve sketching, integration by substitution, introductory differential equations , and applications of the derivative and integral.

#### MAT-152 *Calculus II*
4 credits

**Prerequisites: **MAT 151 or equivalent.

MAT-152 is a continuation of MAT-151. A further study of differential and integral calculus of real functions of one real variable. Topics include further techniques of integration, applications of the integral (volume, arc length, work), and sequences and series.

#### MAT-212 *Advanced Statistical Methods*
3 credits

**Prerequisites: **MAT-112 or equivalent.

A continuation of MAT-112. Topics covered include analysis of variance, multiple regression, chi square and nonparametric statistics, time series, index numbers and decision theory.

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

**Prerequisites: **MAT-105 or equivalent.

Topics include number systems, arithmetic, geometry, and problem solving. The emphasis is on mathematics taught in the elementary classroom, using a variety of teaching techniques, methods, and hands-on materials including manipulatives, calculators and computers.

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

**Prerequisites: **MAT-221 or equivalent.

A continuation of MAT-221 with an emphasis on mathematical concepts and algorithms. Additional topics include descriptive statistics.

#### MAT-251 *Calculus III*
4 credits

**Prerequisites: **MAT-152 or equivalent.

A continuation of MAT-152. A study of real functions of several real variables. Topics include differentiability and continuity, differential geometry, extrema, Lagrange multipliers, multiple integration, line and surface integrals, and the theorems of Green, Gauss and Stokes.

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

**Prerequisites: **MAT-299T Introduction to Proof (any version)

Systems of linear equations, matrix operations, combinatorics, graph theory.

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

**Prerequisites: **Permission

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

#### MAT-298 *Lower Division Seminar*
1
- 3 credits

**Prerequisites: **MAT-299T Introduction to Proof (any version)

Strongly recommended for those planning to major in mathematics and computer science. May be repeated for credit.

#### MAT-299T.10 *Introduction to Proof: Number Theory*
1 credit

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-299T.15 *Introduction to Proof: Combinatorics*
1 credit

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-299T.20 *Introduction to Proof: Sets and Functions*
1 credit

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-299T.25 *Introduction to Proof: Logic*
1 credit

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-311 *Probability & Mathematical Statistics I*
3 credits

**Prerequisites: **MAT-299T Introduction to Proof (any version)

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 & Mathematical Statistics II*
3 credits

**Prerequisites: **MAT-312

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-251 or equivalent.

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-299T Introduction to Proof (any version)

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

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

**Prerequisites: **MAT-299T Introduction to Proof (any version)

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-299T Introduction to Proof (any version)

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 Variables*
3 credits

**Prerequisites: **MAT-299T Introduction to Proof (any version)

A study of the calculus of functions of a complex variable. Topics include elementary functions, series representation, analytic functions, complex integration and conformal mappings.

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

**Prerequisites: **MAT-299T Introduction to Proof (any version)

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-299T Introduction to Proof (any version)

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

#### MAT-461 *Algebraic Structures*
3 credits

**Prerequisites: **MAT-299T Introduction to Proof (any version)

An introduction to the study of abstract algebra. Topics will be primarily from the theory of groups and rings.

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

**Prerequisites: **Permission

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

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

**Prerequisites: **Permission

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

#### 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.