# Mathematics Courses

Mathematics courses are designed to meet two goals: (1) to introduce some of the most influential ideas and techniques in mathematics; and (2) to develop problem-solving ability by teaching students to combine creative mathematical searching with rigorous reasoning. The computer science program includes programming and software design, algorithms, system architectures, operating systems, language theory, databases, and online information systems design. Computer science courses are designed to prepare students for a lifetime of learning that will enable them to move beyond current technology to meet the challenges of the future.

**MATH 005 Algebraic Preliminaries (4)**

Students develop basic computational skills and strengthen their understanding of fundamentals in preparation for courses that involve more difficult quantitative concepts. Students with placement level D must complete this course with a grade of C or higher before attempting MATH 104. Topics include operations on whole and signed numbers, fractions, decimals, exponents, variables, linear equations, and elementary problem solving. Traditional grading only. While students receive no credit for this course, the course grade does count toward their overall grade point average as if it were a 4 semester-hour course. Prerequisite: placement or consent. Offered each spring.

**MATH 104 Algebra and its Applications (4)**

Presents topics in algebra through traditional and applications-based methods. Topics include functions, exponents and scientific notation, linear, exponential, rational and quadratic functions and graphs, systems of equations,quadratic and linear inequalities. Prerequisite: placement level C, Math 005 with a grade of C or higher, or consent. Students must have a TI-83 or TI-84 graphing calculator. Offered each semester.

**MATH 135 Calculus with Precalculus, Part I (4)**

Students learn the basic tools of calculus, why they work, and how to apply them in various contexts. Symbolic, graphical, and numerical approaches are considered. Topics include limits, derivatives, and applications. Includes sufficient coverage of functions and trigonometry to support the study of calculus and of other sciences. The two-course sequence, MATH 135 and 136, is sufficient preparation for MATH 172 Calculus II. Prerequisite: placement level B, MATH 104 with a grade B or higher, or consent. Offered each fall.

**MATH 136 Calculus with Precalculus, Part II (4)**

A continuation of MATH 135. Topics include applications of derivatives, the Riemann integral, and the Fundamental Theorem of Calculus. Includes sufficient instruction in advanced algebraic techniques to support the study of calculus. Prerequisite: MATH 135 with a grade of C-or higher or consent. Offered each spring.

**MATH 150 Topics in Modern Mathematics (4)**

Course exposes students to areas of modern mathematics. Topics vary but may include voting theory, game theory, mathematics and art, elementary number theory, graph theory and scheduling problems, management science, and others. Focus is on critical thinking skills, communicating mathematics orally and in writing, and applications to other disciplines. Prerequisite:placement level A or B. Offered each semester.

**MATH 171 Calculus I (4)**

Students learn the basic tools of calculus, why they work, and how to apply them in various contexts. Calculus I develops the differential calculus through symbolic, graphical, and numerical approaches. Topics include differentiation of algebraic and transcendental functions, applications in modeling and optimization, and the Fundamental Theorem of calculus and an introduction to differential equations. Prerequisite: placement level A or consent. Offered each fall.

**MATH 172 Calculus II (4)**

A continuation of Calculus I. More advanced techniques are studied and used to solve quantitative problems in various contexts. Topics include integration techniques, applications of definite integration, polar coordinates, parametric equations and sequences and series. Prerequisite: MATH 136 or 171 with a grade of C-or higher or consent. Offered each semester.

**MATH 189 Games and Decisions (4)**

In this course, we use discrete mathematics (game theory, logic, probability) to model real-world situations involving decision making. Prerequisite: placement level H, A or B. Offered spring of odd-numbered years.

**MATH 205 Foundations of Logic and Proof (4)
**Introduction to abstract mathematical thinking and logical reasoning skills needed in upper-level Math/CS courses. Topics include logic, argument, proofs, induction, sets, and abstract functions and relations. Emphasizes mathematical writing. Identical to CS 205. Prerequisite: MATH 172 or CS 212 with a grade of C or higher or consent. Recommended spring of sophomore year. Offered each spring.

**MATH 210 Introductory Statistics (4)**

Introduces students to learning from data. Topics include the basics of data production, data analysis, probability, Central Limit Theorem, and statistical inference. Statistical software is used for data management, calculation, and visualization. No previous knowledge of statistics is required. Students cannot receive credit for both MATH 210 and PSY 210. Prerequisites: sophomore status or higher. Placement level B or A or H, or MATH 104 with a grade of C-or higher. Not appropriate for first-year students. Students must have a TI-83 or TI-84 graphing calculator. Offered each semester.

**MATH 217 Linear Algebra (4)**

The study of vector spaces and linear equations in several variables. Topics include systems of linear equations, vector spaces, linear dependence of vectors, bases, dimension, linear transformations, matrices, determinants and applications. Prerequisite: MATH 172 (grade of C-or higher) or consent. Offered each fall.

**MATH 273 Multivariable Calculus (4)**

Topics include functions of several variables, curves, surfaces, partial differentiation, multiple integrals, and vector analysis. Prerequisites: MATH 172 (grade of C-or higher) or consent. Offered each spring.

**MATH 274 Ordinary Differential Equations (4)**

Explores the theory and applications of ordinary differential equations and their solutions. Topics include linear and non-linear first order equations, higher order linear equations, series solutions, systems of linear differential equations, Laplace transforms, and numerical methods. Prerequisite: MATH 172 (grade of C-or higher) or consent. Offered each fall.

**MATH 300 Teaching Assistants' Program for Math (1)**

Qualified students assist math instructors in teaching their classes. Enrollment is by invitation of the MATH/CS department. Although the course is useful for students seeking certification in secondary education, enrollment is not limited to them. A student may enroll more than once, but may apply no more than 3semester hours earned in this manner toward graduation. May not be used to satisfy major or minor requirements in mathematics, although one semester of MATH 300 is required for secondary education certification. Offered each semester.

**MATH 310 Statistical Models (4)**

A course in applied data analysis. Emphasizes construction of models for authentic data sets. Statistical software is used extensively for analyzing real data sets from various contexts. Topics include parametric and non-parametric tests, simple and multiple regression, and ANOVA. Prerequisites: ENG 105 with a grade of C or higher, MATH 172 with a grade C or higher and MATH 210 with a grade C or higher or consent. Offered spring of even numbered years.

**MATH 316 Probability (4)
**Approaches probability as a discipline with applications throughout mathematics and the sciences. Topics include classical and axiomatic probability, random variables, common distributions, density functions, expectation, conditional probability, independence, the Law of Large Numbers, and the Central Limit Theorem. Prerequisites: MATH 273 (grade of C-or higher) or consent. Offered fall of odd-numbered years.

**MATH 319 Algebraic Structures I (4)**

An introduction to algebraic structures focusing on rings and fields. Topics include homomorphisms and isomorphisms, ring structure, equivalence classes, quotient structures and polynomial rings. Prerequisite: MATH/CS 205 (grade of C-or higher) and MATH 217 (grade of C-or higher). Offered each fall.

**MATH 325 Theory of Elem Mathematics I (4)**

Develops a professional knowledge of the mathematics generally taught in elementary schools (K-6). Part I focuses on number systems, arithmetic, number theory and algebraic concepts. Does not count as an elective for any mathematics major. Prerequisites: Any credit-bearing Mathematics course: MATH 150 is highly recommended. Junior/senior status and admission to the program for Elementary or Special Education Teacher Certification. Offered each spring.

**MATH 326 Theory of Elem Mathematics II (4)**

Develops a professional knowledge of the mathematics generally taught in elementary schools (K6). Part II focuses on geometry, probability and statistics. Does not count as an elective in any mathematics major. Prerequisites: MATH 325 (grade of C or higher). Offered each fall.

**MATH 333 Number Theory (4) W**

An introduction to the study of the set of natural numbers. Topics may include linear congruence, greatest common divisor, Euler’s totient function, Chinese Remainder Theorem, Fermat’s Little Theorem, Wilson’s Theorem, Legendre symbol, and quadratic reciprocity. Prerequisites: ENG 105 with a grade of C or higher and MATH/CS 205 (grade of C-or higher) or consent. Offered fall of odd-numbered years.

**MATH 340 Modern Geometries (4)**

Explores Euclidean and non-Euclidean geometries and the cultural impact of non-Euclidean geometries. Topics may include geodesics, plane geometry, non-Euclidean geometries, finite geometries, complex numbers, and geometric transformations. Prerequisites: MATH/CS 205 (grade of C-or higher), MATH 217 (grade of C-or higher), or consent. Offered spring of odd-numbered years.

**MATH 350 Numerical Methods (4)**

Examines efficient methods used in solving numerical problems with the aid of a computer. Topics include floating point arithmetic, interpolation and approximation, integration, roots of non-linear equations, ordinary differential equations, and systems of linear equations. Prerequisites: MATH 172 (grade of C-or higher) and CS 112 (grade of C or higher), or consent. Identical to CS 350. Offered spring of even-numbered-years.

**MATH 410 Mathematical Models (4)W**

An introduction to mathematical models and sensitivity analysis. Emphasizes construction of models for real world applications in a variety of area. Mathematical software is used extensively for problem solving. Topics include optimization models, linear and discrete programming, dynamic models and probability models. Prerequisites: ENG 105 with a grade of C or higher, MATH 217 and MATH 273 with grade of C-or better. Offered fall of even-numbered years

**MATH 419 Algebraic Structures II (4)**

A continuation of Algebraic Structures I, focusing on groups, homomorphism theorems and Galois Theory. Prerequisite: MATH 319 (grade of C-or higher). Offered spring of even-numbered years.

**MATH 470 Internship in Mathematics (2 or 4)**

An intensive mathematics project conducted in a professional setting. Pass/Fail only. Prerequisites: junior/senior status, cumulative GPA of at least 2.5 and consent. Offered on demand.

**MATH 471 Real Analysis (4)**

A theoretical treatment of continuity and real-valued functions. Topics may include sequences, series, limits, the derivative and the integral. Prerequisite: MATH 319 (grade of C-or higher). Offered spring of odd-numbered years.

**MATH 480 Advanced Topics in Mathematics (4)**

Enables students to explore areas of advanced mathematics which are otherwise not included in the curriculum. Students may repeat the course for credit as the topic varies. Prerequisite: consent. Offered intermittently.

**MATH 487 Mathematics Senior Seminar (1)**

Students read and discuss current journal articles in mathematics. Topics vary and may include problem solving. Pass/fail grading. Prerequisites: declared mathematics major and senior status or consent. Offered each spring.

**MATH 489 Research in Mathematics (2 or 4)**

Offers students the opportunity to conduct original scientific research in an area of interest. Students work closely with one or more members of the natural science faculty to develop and conduct a research project, then present their findings orally during the semester’s undergraduate research symposium and as a formal research paper. Students are encouraged to present their findings at a conference. Prerequisite: junior/senior status and a major in mathematics, prior approval by the project advisor, and consent of the instructor. Students may enroll for 2 or 4 hours in a given semester. May be repeated for a maximum total of 8 semester hours. Identical to BIO 489, CHEM 489, CS 489, and EES 489. Offered each semester and most January Terms (2 semester hours only).