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Professor: E. Knapp
Assistant Professors: J. Smith (Chair), T. Sorenson
The Mathematics curriculum is designed to provide for the educational needs of many students. For general education there are courses which develop basic competence in mathematical reasoning. More advanced courses furnish necessary mathematical background for a variety of majors. A major in Mathematics suits students intending to become mathematics teachers, planning to enter certain professions in business or industry, preparing for graduate study in mathematics or related areas, or simply wishing to support another major.
MATHEMATICS MAJOR: 41 credit hours
Required Courses: 33 credit hours
MATH 151 - Calculus I (4 cr)
MATH 152 - Calculus II (4 cr)
MATH 153 - Calculus III (3 cr)
MATH 200 - Foundations of Mathematics (3 cr)
MATH 220 - Linear Algebra (3 cr)
MATH 490 - Senior Seminar (1 cr)
*MATH 300-level Elective courses (3 courses) (9 cr)Two of the following courses:
MATH 340 - Abstract Algebra (3 cr)
MATH 345 - Topology (3 cr)
MATH 350 - Real Analysis (3 cr)
MATH 355 - Complex Analysis (3 cr)
*May use the two courses not used for the elective area above.
Required Supportive Courses: 8 credit hours
COSC 210 - Computer Science I (4 cr)
PHYS 221 - General Physics I (4 cr)
MATHEMATICS MINOR: 18 credit hours
MATH 152 - Calculus II (4 cr)
MATH 200-level Elective (or higher) (3 cr)
*MATH Elective courses (11 cr)
*One Computer Science course allowed as a substitute.
MATHEMATICS COURSES:
MATH 110 - STRUCTURE OF MATHEMATICS (3 credits)
Recommended for Elementary Education majors as a preliminary to MATH 113. An introduction to basic
mathematical ideas including counting and measuring, calculation, symbol manipulation, algebra and logic.
Topics are matched to the elementary school curriculum. The emphasis is on developing understanding, intuition,
and imagination rather than rigidly following prescribed methods.
NOTE: OFFERED EVERY SEMESTER
MATH 113 - METHODS OF TEACHING ELEMENTARY MATHEMATICS (3 credits)
The structure of arithmetic based on the properties of the natural number system is presented. Samples of
concrete materials for different grade levels are demonstrated. Alternate approaches to solving problems
and performing basic operations are proposed. Visualization of concepts is stressed. Emphasis throughout
the course is on teaching mathematics for understanding of theory and application.
NOTES: RECOMMENDED PREREQUISITE: MATH 110
OFFERED EVERY SEMESTER
MATH 115 - MATHEMATICS, SCIENCE, AND TECHNOLOGY (4 credits)
A course for Elementary and Middle School Education majors in their junior and senior year. Meets SD
certification requirements for 1 credit in natural science and 3 credits in mathematics. Space and earth
science is the context for learning math concepts. The science starts with our universe and works down to
our moon and planet Earth. Among the math topics are measurement, data collection, curve fitting, spatial
sense, and geometry.
NOTES: PREREQUISITE: BIOL 200
OFFERED MOST INTERIMS
MATH 140 - QUANTITATIVE REASONING (Area 2.3) (3 credits)
For students with one or two years of high school algebra. This course is at the level of college algebra but
is not focused on algebra. It stresses application of mathematics in careers of non-scientists and in the
everyday lives of educated citizens, covering basic mathematics, logic, and problem solving in the context
of real-world applications. Topics that often arise in the course include numerical literacy, probability,
statistics, financial management, modeling, and mathematics in arts, science, and government.
NOTE: OFFERED EVERY SEMESTER
MATH 150 - PRE-CALCULUS (Area 2.3) (4 credits)
Algebra review, functions and graphs, logarithmic and exponential functions, analytic geometry,
trigonometric functions, trigonometric identities and equations, mathematical induction, complex numbers.
Students completing this course are prepared to enter calculus.
NOTE: OFFERED EVERY SEMESTER
MATH 151 - CALCULUS I (Area 2.3) (4 credits)
Limits and continuity for functions of one real variable. Derivatives and integrals of algebraic,
trigonometric, exponential, and logarithmic functions. Applications of the derivative. Introduction to
related numerical methods.
NOTE: OFFERED EVERY SEMESTER
MATH 152 - CALCULUS II (4 credits)
Techniques of integration, numerical integration, and applications of integrals. Infinite series including
Taylor series. Introduction to differential equations. Calculus in polar coordinates.
NOTE: OFFERED EVERY SEMESTER
MATH 153 - CALCULUS III (3 credits)
The calculus of vector-valued functions, functions of several variables, and vector fields. Includes vector
operations, equations of curves and surfaces in space, partial derivatives, multiple integrals, line integrals,
surface integrals, and applications.
NOTE: OFFERED EVERY SPRING SEMESTER
MATH 200 - FOUNDATIONS OF MATHEMATICS (3 credits)
Bridges the gap between computational , algorithmic mathematics courses and more abstract, theoretical
courses. Emphasizes the structure of modern mathematics: axioms, postulates, definitions, examples
conjectures, counterexamples, theorems, and proofs. Builds skill in reading and writing proofs. Includes
careful treatment of sets, functions, relations, cardinality, and construction of the integers, and the rational,
real, and complex number systems.
NOTES: PREREQUISITE: MATH 152
OFFERED EVERY FALL SEMESTER
MATH 220 - LINEAR ALGEBRA (3 credits)
Vector spaces, linear independence, basis and dimension, linear mappings, matrices, linear equations,
determinants, Eigen values, and quadratic forms.
NOTES: PREREQUISITE: MATH 152
OFFERED EVERY SPRING SEMESTER
MATH 310 - DIFFERENTIAL EQUATIONS (3 credits)
Methods of solving first and second order differential equations, applications, systems of equations, series
solutions, existence theorems, numerical methods, and partial differential equations.
NOTES: PREREQUISITE: MATH 152
OFFERED EVERY FALL SEMESTER
MATH 315 - PROBABILITY AND STATISTICS (3 credits)
Probability as a mathematical system, random variables and their distributions, limit theorems, statistical
inference, estimation, decision theory and testing hypotheses.
NOTES: PREREQUISITE: MATH 152
OFFERED OCCASIONALLY
MATH 320 - DISCRETE STRUCTURES (3 credits)
Topics to be selected from counting techniques, mathematical logic, set theory, data structures, graph
theory, trees, directed graphs, algebraic structures, Boolean algebra, lattices, and optimization of discrete
processes.
NOTES: PREREQUISITES: MATH 151 AND COSC 210
OFFERED EVERY SPRING SEMESTER
MATH 330 - HISTORY OF MATHEMATICS (W - Area 2.1B) (3 credits)
The history of mathematics from ancient to modern times. The mathematicians, their times, their problems,
and their tools. Major emphasis on the development of geometry, algebra, and calculus.
NOTES: PREREQUISITE: MATH 200
OFFERED INTERIM, ODD YEARS
MATH 335 - MODERN GEOMETRY (3 credits)
Areview of Euclidean geometry, an examination of deficiencies in Euclidean geometry, and an introduction
to non-Euclidean geometrics. Axiomatic structure and methods of proof are emphasized.
NOTES: PREREQUISITE: MATH 200
OFFERED INTERIM, EVEN YEARS
MATH 340 - ABSTRACT ALGEBRA (3 credits)
Asurvey of the classical algebraic structures taking an axiomatic approach. Deals with the theory of groups
and rings and associated structures, including subgroups, factor groups, direct sums of groups or rings,
quotient rings, polynomial rings, ideals, and fields.
NOTES: PREREQUISITE: MATH 200 AND MATH 220
OFFERED FALL SEMESTER, EVEN YEARS
MATH 345 - TOPOLOGY (3 credits)
An introduction to topological structures from point-set, differential, algebraic, and combinatorial points of
view. Topics include continuity, connectedness, compactness, separation, dimension, homeomorphism,
homology, homotopy, and classification of surfaces.
NOTES: PREREQUISITE: MATH 200 AND MATH 220
OFFERED SPRING SEMESTER, ODD YEARS
MATH 350 - REAL ANALYSIS (3 credits)
This course develops the logical foundations underlying the calculus of real-valued functions of a single
real variable. Topics include limits, continuity, uniform continuity, derivatives and integrals, sequences and
series of numbers and functions, convergence, and uniform convergence.
NOTES: PREREQUISITE: MATH 200 AND MATH 220
OFFERED FALL SEMESTER, ODD YEARS
MATH 355 - COMPLEX ANALYSIS (3 credits)
A study of the concepts of calculus for functions with domain and range in the complex numbers. The
concepts are limits, continuity, derivatives, integrals, sequences, and series. Topics include Cauchy-
Riemann equations, analytic functions, contour integrals, Cauchy integral formulas, Taylor and Laurent
series, and special functions.
NOTES: PREREQUISITE: MATH 200 AND MATH 220
OFFERED SPRING SEMESTER, EVEN YEARS
MATH 197, 297, 397 - TOPICS IN MATHEMATICS (2-4 credits)
MATH 199, 299, 399 - INDEPENDENT STUDY (2-4 credits)
MATH 490 - SENIOR SEMINAR (1 credit)
This course reviews and correlates the courses in the mathematics major. Each student is responsible for
preparing the review of one area. Students also read papers from contemporary mathematics journals and
present them to the class. The course uses the ETS mathematics major exam.
NOTES: PREREQUISITE: MATH 200, MATH 220, AND SENIOR STANDING
OFFERED EVERY SPRING SEMESTER