**MATH 205 – Foundations of Mathematics
**Instructor: Professor Lakins

An introduction to concepts encountered in the study of abstract mathematics. Topics covered include logic, mathematical proofs, set theory, relations, functions, mathematical induction, and introductory number theory. The concepts of injectivity, surjectivity, and inverses are discussed as well as elementary computational tools such as the Division Algorithm and Euclid’s algorithm for the greatest common divisor. Additional topics may include cardinality, combinatorics, graph theory, algebraic structure, the real number system, and concepts of mathematical analysis.

*Prerequisite*: MATH 152 or MATH 160 with a grade of C or better.

*Distribution Requirements*: ME, SP.

**MATH 211 – Vector Calculus and Several Variable Integration
**Instructor: Professor Carswell

A study of integration of functions of several variables, including the use of polar, cylindrical, and spherical coordinate systems; and vector calculus, including vector fields, line and surface integrals, and the theorems of Green and Stokes.

*Prerequisite*: MATH 152 with a grade of C or better.

*Distribution Requirement*s: QR.

May not be taken for credit if a grade of C or better in MATH 210 has already been received.

**MATH 270 – Optimization and Approximation
**Instructor: Professor Ellers

A study of optimization of functions of one variable and of several variables, including the Extreme Value Theorem and Lagrange multipliers; sequences and series; and Taylor approximation of functions.

*Prerequisite*: MATH 152 with a grade of C or better.

*Distribution Requirements*: QR.

May not be taken for credit if a grade of C or better in MATH 170 has already been received.

**MATH 280 – Ordinary Differential Equations
**Instructor: Professor Carswell

An examination of methods of solving ordinary differential equations with emphasis on the existence and uniqueness of solutions of first order equations and second order linear equations. Topics may include Laplace transforms, systems of linear differential equations, power series solutions, successive approximations, linear differential equations, and oscillation theory with applications to chemistry and physics.

*Prerequisit*e: MATH 152 or MATH 210 with a grade of C or better.

*Distribution Requirements*: SP.

**MATH 325 – Algebraic Structures I
**Instructor: Professor Werner

An introduction to the notion of an algebraic structure concentrating on the simplest such structure, that of a group. Rings and fields are also discussed.

*Prerequisite*: MATH 205 and MATH 320, each with a grade of C or better.

*Distribution Requirements*: SP.

**MATH 340 – Introduction to Analysis
**Instructor: Professor Weir

An examination of the theory of calculus of a single variable. Topics include properties of the real numbers, topology of the real line, and a rigorous treatment of sequences, functions, limits, continuity, differentiation and integration.

*Prerequisite*: MATH 205 with a grade of C or better, and a grade of C or better in one of the following courses: MATH 210, MATH 211, MATH 270, MATH 280.

Distribution Requirements: SP.

**MATH 345 – Probability and Statistical Inference I
**Instructor: Professor Lo Bello

A study of mathematical models, sample space probabilities, random variables, expectation, empirical and theoretical frequency distributions, moment generating functions, sampling theory, correlation and regression.

*Prerequisite*: MATH 152 or MATH 210 with a grade of C or better.

*Distribution Requirements*: SP.

This is one of the possible mathematics courses that may be substituted for one of the required 300-level CMPSC courses in the Computer Science major.

**MATH 370 – Graph Theory and Combinatorics **New Course**
**Instructor: Professor Dodge

A study of finite graphs and combinatorics, covering enumeration of combinatorial structures, directed and undirected graphs, and recursive algorithms. Topics include trees, planarity, graph coloring, Eulerian and Hamiltonian graphs, shortest path algorithms, the pigeonhole principle, permutations and combinations of finite sets and multisets, binomial and multinomial coefficients, and the inclusion-exclusion principle.

*Prerequisites*: MATH 205 with a grade of C or better

*Distribution Requirements*: SP

This is one of the mathematics courses that may be substituted for one of the required 300-level CMPSC courses in the Computer Science major.