Southwestern

Engaging Minds, Transforming Lives

Math & Computer Science

Mathematics

The Mathematics curriculum is traditional, although many of the best reform ideas (technology, group projects, writing mathematics, etc.) are being incorporated where appropriate to enhance the traditional topics.

The following list of courses represents current or recent course offerings. See the course catalog for updated information.

  • 52-001 SELECTED TOPICS
    May be repeated with change in topic.
  • 52-002 SELECTED TOPICS
    May be repeated with change in topic.
  • 52-003 SELECTED TOPICS
    May be repeated with change in topic.
  • 52-004 SELECTED TOPICS
    May be repeated with change in topic.
  • 52-104 EXPLORATIONS IN MATHEMATICS
    This course presents the spirit and beauty of mathematics through topics chosen by the instructor, emphasizing the role that mathematics plays in society. Topics may include mathematics in art and literature, Euclid's Elements, game theory and voting theory. The mathematical content may include geometry, algebra, and number systems. The course is suitable for a general audience with a broad spectrum of backgrounds and abilities and also satisfies requirements for EC-6 or 4-8 teacher certification. This course may not be used for the Mathematics major or minor. (Fall, each year; and Spring, odd years) (NS)
  • 52-114 INTRODUCTION TO STATISTICS
    This course provides students in the social and biological sciences with the skills necessary to perform elementary statistical analysis. Topics include descriptive measures, probability, sampling theory, random variables, binomial and normal distributions, estimation and hypothesis testing, analysis of variance, regression and correlation. This course may not be used for the Mathematics major or minor. (Each semester) (NS)
  • 52-124 ELEMENTARY FUNCTION THEORY
    This course investigates relations, functions and general properties of functions. Some of the elementary functions considered are polynomials, rational functions, exponentials, logarithms and trigonometric functions. An objective of this course is to prepare students for Calculus I. This course may not be used for the Mathematics major or minor. (Fall) (NS)
  • 52-150 FLIPPED CALCULUS I LAB
  • 52-154 CALCULUS I
    This is a first course in single variable differential and integral calculus. Topics include limits, continuity, differentiation, integration, the Fundamental Theorem of Calculus, the method of substitution, and applications (e.g., optimization, related rates, consequences of the Mean Value Theorem). Prerequisite: Mastery of high school-level pre-calculus (algebra, trigonometry, exponential and logarithmic functions). (Each semester) (NS)
  • 52-204 TOPICS IN MATHEMATICS
    This course investigates a topic in Mathematics that varies according to the interests of professor. This course may be repeated with a change in the topic. (NS)
  • 52-254 CALCULUS II
    Topics include techniques of integration, applications of integration (e.g., volumes of solids of revolution, arc length, work), improper integrals, introductory differential equations, infinite series, power series, Taylor's Theorem, and polar coordinates. Prerequisite: Mathematics 52-154. (Each semester) (NS)
  • 52-291 PUTNAM POWER HOUR
    This course is designed to sharpen problem solving abilities. Students will tackle challenging problems from the William Lowell Putnam Competitions of previous years and study some of the published solutions. Students enrolled in this course will be encouraged to compete in the Putnam Competition in early December. This course may be repeated for credit, but may not be counted toward the major or minor, and must be taken P/D/F. Prerequisite: Consent of instructor.
  • 52-301 SELECTED TOPICS
    May be repeated with change in topic. Prerequisite: Permission of instructor.
  • 52-302 SELECTED TOPICS
    May be repeated with change in topic. Prerequisite: Permission of instructor.
  • 52-303 SELECTED TOPICS
    May be repeated with change in topic. Prerequisite: Permission of instructor.
  • 52-304 SELECTED TOPICS
    May be repeated with change in topic. Prerequisite: Permission of instructor.
  • 52-354 CALCULUS III
    This is a course in multivariable calculus. Topics include vectors, vector-valued functions and functions of several variables, partial differentiation, multiple integration, applications of partial differentiation, applications of multiple integrals, line integrals, Green's Theorem, and surface integrals. Prerequisite: Mathematics 52-254. (Fall, every year; Spring, even years) (NS)
  • 52-384 DISCRETE MATHEMATICS
    See Computer Science 54-384. (Fall) (NS)
  • 52-404 GEOMETRY
    This course investigates various approaches to geometry. Topics may include synthetic geometry, analytic geometry, projective geometry, Euclidean geometry and non-Euclidean geometry. Prerequisite: Permission of instructor. (Fall, even years) (NS)
  • 52-414 OPERATIONS RESEARCH
    See Computer Science 54-414 and Business 30-414.
  • 52-524 INTRODUCTION TO NUMERICAL ANALYSIS
    This course investigates the derivations and applications of numerical techniques most frequently used by scientists: interpolation, approximation, numerical differentiation and integration, zeroes of functions and solution of linear systems. It is cross-listed as Computer Science 54-524. Prerequisites: Mathematics 52-254, 52-674, and Computer Science 54-184, or permission of instructor. (Spring, odd years) (NS)
  • 52-574 PROBABILITY AND MATHEMATICAL STATISTICS
    This course is a calculus-based, mathematical introduction to the fundamental principles of probability theory and applications. Topics include combinatorial analysis used in computing probabilities, the axioms and properties of probability, conditional probability, independence of events, discrete and continuous random variables, the standard distributions, expected value and variance, joint distributions, distributions of a function of a random variable, and sampling distributions. Also included are theoretical results such as Bayes Theorem, Central Limit Theorem, Law of Large Numbers, the Empirical Rule, Hypothesis Testing and Confidence intervals at least for a single mean and a single proportion . Prerequisite: Mathematics 52-254. (Spring) (NS)
  • 52-674 LINEAR ALGEBRA
    This course is an introduction to the basic structure of proofs, linear equations and matrices, vector spaces, linear mappings, determinants, quadratic forms, vector products and groups of symmetries. Prerequisite: Mathematics 52-154 and one approved MAT or CSC course at the 200-level or above, or permission of instructor. (Each semester) (NS)
  • 52-684 ALGEBRAIC STRUCTURES I
    This course investigates the theory of sets, relations, functions, groups and rings. A rigorous approach to learning and writing proofs is emphasized. Prerequisite: Mathematics 52-674 or permission of instructor. (Fall) (NS)
  • 52-694 ALGEBRAIC STRUCTURES II
    This course investigates rings of polynomials and algebraic field theory. Topics include quotient rings, isomorphism theorems, extension fields and Galois theory. Prerequisite: Mathematics 52-684. (Spring, odd years) (NS)
  • 52-754 DIFFERENTIAL EQUATIONS I
    This course investigates the theory and application of differential equations. Topics include first order differential equations, separable equations, exact equations, linear differential equations of order n>1, homogeneous equations with constant coefficients, nonhomogeneous equations, the method of undetermined coefficients, variation of parameters, power series solutions and an introduction to Laplace transforms. Prerequisite: Mathematics 52-354, or permission of instructor. (Spring) (NS)
  • 52-764 DIFFERENTIAL EQUATIONS II
    This course investigates further topics in differential equations. Topics include the Laplace transform, linear systems, numerical solutions, nonlinear systems and Fourier Series analysis of partial differential equations with boundary conditions. Prerequisites: Mathematics 52-674 and 52-754 or permission of instructor. (Fall, odd years) (NS)
  • 52-834 COMPLEX ANALYSIS
    This course investigates the algebra and geometry of complex numbers. Topics include analytic and harmonic functions, series, contour integration, conformal maps and transformations. Prerequisite: Mathematics 52-354 or permission of instructor. (Fall, even years) (NS)
  • 52-844 SEMINAR IN SPECIAL TOPICS
    This course is a limited enrollment seminar in a major area of mathematics not generally covered in other courses. Topics may include but are not limited to advanced analysis, combinatorics, logic and history of mathematics. The course may be repeated for credit as topics vary. Prerequisite: Three courses at the 200 level or above and permission of instructor. (NS)
  • 52-854 REAL ANALYSIS I
    This course investigates the algebra and topology of the real numbers. Topics include completeness, sequences, limits and continuity, differentiation, the Mean-Value Theorem, Taylors Theorem and infinite series. May also include sequences and series of functions. A rigorous approach to learning and writing proofs is emphasized. Prerequisite: Mathematics 52-674, or permission of instructor. (Fall) (NS)
  • 52-864 REAL ANALYSIS II
    This course is a continuation of Real Analysis I. Topics vary but may include the theory of Riemann integration, Lebesgue integration, sequences and series of functions, Fourier analysis, function spaces. Prerequisite: Mathematics 52-854 or permission of instructor. (Spring, even years) (NS
  • 52-884 TOPOLOGY
    This course is a study of the topology of the line and plane. Topics include limit points, open sets, closed sets, connectedness, compactness, continuous functions and homeomorphisms. Prerequisite: Mathematics 52-254. (Fall, odd years) (NS)
  • 52-894 SENIOR SEMINAR IN MATHEMATICAL MODELING
    This course will fulfill the capstone requirement in Mathematics. Since it serves as a culmination of the students undergraduate mathematical experience, a balance is sought between application and theory. Topics may include optimization methods with sensitivity analysis, numerical and analytic methods, linear and non-linear differential and difference equations, curve and surface fitting, statistics, and stochastic methods. Topics may vary with the instructor. Applications will be taken from the social and natural sciences. Collaboration and significant class participation are expected. Each student will take the Major Field Test. A major semester project resulting in a written paper and an oral presentation is required from each student; an external presentation may also be required.. Prerequisites: Six courses in the major at the 300 level or above, Computer Science 54-184, and permission of instructor. (Fall) (NS) (WA)
  • 52-901 TUTORIAL
  • 52-902 TUTORIAL
  • 52-903 TUTORIAL
  • 52-904 TUTORIAL
  • 52-951 INDEPENDENT STUDY
  • 52-952 INDEPENDENT STUDY
  • 52-953 INDEPENDENT STUDY
  • 52-954 INDEPENDENT STUDY
  • 52-984 HONORS
    By invitation only.