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University of Wyoming

University of Wyoming Math Department Upper Division Undergraduate Math Course Descriptions

Upper Division MATH Courses

Math 2250 Elementary Linear Algebra
Math 2300 Discrete Structures
Math 2310 Applied Differential Equations I
Math 2800 Math Major Seminar
Math 2850 Putnam Team Seminar
Math 3000 Fundamental Concepts of Mathematics
Math 3200 Polynomials
Math 3310 Applied Differential Equations II
Math 3500 Applied Algebra
Math 3550 Introduction to Abstract Algebra
Math 4000 History of Mathematics
Math 4100 Mathematics in the Elementary School
Math 4150 Secondary School on Campus
Math 4200 Mathematics Analysis I
Math 4205 Mathematics Analysis II
Math 4230 Introduction to Complex Analysis
Math 4250 Mathematical Theory of Probability
Math 4260 Introduction to the Theory of Statistics
Math 4300 Introduction to Mathematical Modeling
Math 4340 Numerical Analysis
Math 4400 Vector Calculus
Math 4420 Advanced Logic
Math 4440 Introduction to Partial Differential Equations
Math 4500 Matrix Theory
Math 4550 Introduction to the Theory of Numbers
Math 4600 Foundations of Geometry

MATH 2250: Elementary Linear Algebra (3 hrs)

Course Description: Studies linear equations and matrices, vector spaces, linear transformations, determinants, orthogonality, eigenvalues and eigenvectors.
Prerequisite: grade of C or better in MATH 2200 or 2350.

MATH 2300: Discrete Structures (3 hrs) [This class does not count toward a math major.]

Course Description: Introduces the mathematical concepts that serve as foundations of computer science: logic, set theory, relations and functions, graphs (directed and undirected), inductively defined structures (lists and trees), and applications of mathematical induction. Provides an introduction to abstract and rigorous thinking in advanced mathematics and computer science. Cross listed with COSC 2300.
Prerequisite: grade of C or better in COSC 1030, MATH 2200 or 2350.

MATH 2310: Applied  Differential Equations I (3 hrs)

Course Description: Combines with MATH 3310 for one-year series in applied mathematics. Includes solution of ordinary differential equations, integral transforms. Emphasizes construction of mathematical models arising in physical science and other areas.
Prerequisite: grade of C or better in MATH 2205.

MATH 2800: Mathematics Major Seminar (2 hrs)  

Introduces mathematics majors and mathematics minors to mathematical investigation and discovery. Typically, a range of topics are covered; may include reading assignments and group or individual work on projects for presentation.
 

MATH 2850: Putnam Team Seminar (2 hrs)

Course Description: Preparation for the William Lowell Putnam Mathematical Competition. Problem solving strategies and mathematical content appropriate for the Putnam Exam are emphasized with problem sets taken from previous Putnam or other international math contests. Offered fall semester.
Prerequisites: grade of C or better in MATH 2200 and 2205

MATH 3000: Fundamental Concepts of Mathematics (3 hrs)

Course Description: An introduction to mathematical proof. Topics include elements of propositional logic, naïve set theory, and proof techniques such as direct proof, proof by contrapositive, mathematical induction, and proof by contradiction. Explores applications of these concepts to number theory, mathematical analysis, and other branches of mathematics. Offered fall semester.
Prerequisite: grade of C or better in MATH 2250.

MATH 3200: Polynomials (3 hrs)

Rigorous study of polynomials, including an introduction to mathematical proof. Includes basic properties of polynomials and their roots together with connections to algebra, analysis, geometry, number theory, and numerical analysis. Offered spring semester.
Prerequisite: grade of C or better in MATH 2250

MATH 3310: Applied Differential Equations II (3 hrs)

Course Description: Continues MATH 2310. Includes partial differential equations, Fourier series, boundary value problems, series solutions of ordinary differential equations, linear algebra, linear systems of equations and numerical methods.
Prerequisites: grade of C or better in MATH 2210 and 2310.

MATH 3500: Applied Algebra (3 hrs)

Course Description: Shows how uses of algebraic structures in computer science and physical sciences has increased dramatically in recent years. Introduces some of these structures (partial orderings, groups, codes, fields and algebras) and their applications to other disciplines. Offered fall semester.
Prerequisites: grade of C or better in MATH 2250 and 2300 or 3200 or 3000

MATH 3550: Introduction to Abstract Algebra (3 hrs)

Course Description: Provides basic introduction to groups, rings and fields. Emphasizes axiomatic development. Includes applications to number theory and geometry. Offered spring semester.
Prerequisites: grade of C or better in MATH 3200 or 3000

MATH 4000: History of Mathematics (3 hrs)

Course Description: Explores the roots of mathematics, and the people who made significant contributions to it. Mathematical subjects typically include algebra, calculus and number theory; both chronological and topical approaches are employed. Offered spring semester.
Prerequisites: grade of C or better in MATH 2205.

MATH 4100: Mathematics in the Elementary School (1-6 hrs)

Course Description: Acquaints prospective or experienced teachers of mathematics with newer developments in mathematics curriculum and materials. Emphasizes mathematical basis for courses in elementary mathematics curriculum; organization and design of mathematics programs for grades K-7; and design and construction of curriculum and/or materials to meet specific needs of the teacher or school district.
Prerequisites: grade of C or better in MATH 1105 and consent of instructor

MATH 4150: Secondary School on Campus (1-4 hrs)

Course Description: This course provides prospective teachers opportunity to study mathematics as it relates to the secondary school. Topics may vary from semester to semester. Emphasizes current trends and concerns of secondary school mathematics education. Offered fall semester only.
Prerequisites: grade of C or better in MATH 2205 and 3200 or 3000

MATH 4200: Mathematical Analysis I (3 hrs)
Course Description: Combines with MATH 4205 for a one-year series providing rigorous treatment of the foundations of mathematical analysis. Includes discussion of properties of real numbers, set theory, elementary metric space topology, series and sequences, limits, continuity, differentiation, Riemann and Riemann-Stieltjes integration, sequences and series of functions, equicontinuity, functions of severable variables, inverse and implicit function theorems, and multi-dimensional integration theory. Offered fall semester.
Prerequisites: grade of C or better in MATH 2250 and 2210 and either 3200 or 3000.
MATH 4205: Mathematical Analysis II (3 hrs)
Course Description: Continues MATH 4200. Offered spring semester.
Prerequisite: grade of C or better in MATH 4200
MATH 4230: Introduction to Complex Analysis (3 hrs)
Course Description: Develops the theory of functions of one complex variable. Topics include the algebra and geometry of complex numbers, functions of one complex variable, elementary functions, limits, continuity and differentiation. Differentiability leads to the Cauchy theorem, integral theorems, power series, residue theory, applications to integration theory, and boundary value problems. Offered spring semester.
Prerequisite: grade of C or better in MATH 2210
MATH 4250: Mathematical Theory of Probability (3 hrs)
Course Description: Calculus-based. Introduces mathematical properties of random variables. Includes discrete and continuous probability distributions, independence and conditional probability, mathematical expectation, multivariate distributions and properties of normal probability law. Cross listed with STAT 4250.
Prerequisites: grade of C or better in MATH 2210.
MATH 4260: Introduction to the Theory of Statistics (3 hrs)
Course Description: Presents derivations of theoretical and sampling distributions. Introduces theory of estimation and hypothesis testing. Cross listed with STAT 4260.
Prerequisites: grade of C or better in MATH 4250.

MATH 4300: Introduction to Mathematical Modeling (3 hrs)

Course Description: A model of a real world problem captures the essential features of the problem, while scaling it down to a manageable size. In this course, symbolic tools and mathematical techniques are used to construct, analyze and interpret various mathematical models which arise from problems in the physical, biological and social sciences. Offered fall semester only.
Prerequisites: grade of C or better in MATH 2250 or 3310.

MATH 4340: Numerical Analysis (3 hrs)

Course Description: Considers computer methods and their accuracy for applied mathematics. Topics include machine arithmetic, analysis of rounding error, solution methods for linear systems and nonlinear equations, interpolations, numerical differentiation and integration, and numerical solution of differential equations. Will include some programming. Cross listed with COSC 4340. Offered spring semester.
Prerequisites: grade of C or better in COSC 1010, MATH 2310, and either MATH 2250 or 3310; or consent of instructor.

MATH 4400: Vector Calculus (3 hrs)

Course Description: Offers less rigorous treatment of multivariable calculus than MATH 4205. Includes sequences and series of functions, power series and Taylor's theorem, partial differentiation, implicit functions, Lagrange multipliers, double and triple integrals, vector fields, line and surface integrals and applications to fluid flow, divergence and gradients. Offered fall semester.
Prerequisites: grade of C or better in MATH 2250 or 3310 and 2210

MATH 4420: Advanced Logic (3 hrs)

Course Description: Studies advanced topics in mathematical logic. Takes up such topics as: uninterrupted calculi and the distinctive contributions of syntax and semantics; methatheory, including completeness and consistency proofs; modal logic and semantics; logic as a philosophical tool. Cross listed with COSC/PHIL 4420.
Prerequisites: grade of C or better in PHIL 3420 or equivalent.

MATH 4440: Partial Differential Equations I (3 hrs)

Course Description: Includes first-order partial differential equations, classification of second-order equations and canonical forms, elementary elliptical, hyperbolic and parabolic boundary value problems, transform methods, series solutions and Green's functions. Offered spring semester only.
Prerequisites: grade of C or better in MATH 2210 and 2310

MATH 4500: Matrix Theory (3 hrs)

Course Description: Continuation from MATH 2250 of the study of matrices, an important tool in statistics, physics, engineering and applied mathematics in general. Concentrates on the structure of matrices, including diagonalizability; symmetric, hermitian and unitary matrices; and canonical forms such as Jordan form. Offered fall semester.
Prerequisite: grade of C or better in MATH 2250.

MATH 4550: Theory of Numbers (3 hrs)

Course Description: Studies topics in mathematics which are motivated by questions about integers. Topics include divisibility, congruences, diophantine equations, quadratic residues, primitive roots, primes, and representations of positive integers. Offered spring semester.
Prerequisites: grade of C or better in MATH 3000 or 3200.

MATH 4600: Foundations of Geometry (3 hrs)

Course Description: Broadens the student's understanding of the many faces of geometry and provides a context for the specific case of Euclidean geometry. Various approaches will be presented, including axiomatic, synthetic, coordinate, and transformational methods. Offered fall semester.
Prerequisites: grade of C or better in MATH 3200 or 3000.