Mathematics (MTH)

Professor Grasman and Huang; Emeritus Professor Casler; Instructors Stalzer-Koch, Overholt and Hohman.

The Department of Mathematics seeks to contribute to the educational mission of Heidelberg University by providing: 1. instruction in mathematics as a major/minor area of study; 2. service courses for other departments in which mathematics is considered a vital tool; 3. the necessary mathematics preparation for prospective elementary and secondary school teachers.

Major: 32 semester hours in mathematics courses numbered 222 or above, including 222, 223, 307, 308, 390, 490, and one course selected from 401, 402, 403, and 404. Note: MTH 390 satisfies the Junior Level Discipline Specific Communication Requirement, and MTH 490 satisfies the Senior Capstone Experience. The MTH 390 requirement and the associated 1 semester hour will be waived if a student satisfies the junior level speaking and writing requirement in any other department. The MTH 490 requirement and the associated 1 semester hour will be waived if a student satisfies the capstone requirement in the completion of a second major.

Allied Courses: PHY 101, CPS 150, any CPS course numbered over 200, and one additional course selected from the departments of Biology, Chemistry, Computer Science, Philosophy and Physics. Candidates for the education license in Integrated Math for Adolescent to Young Adults (AYA) must include CPS 201. 

Minor: 15 semester hours which must include MTH 222, 223; remaining hours must be 300 level or above. The prerequisite for MTH 222 is MTH 121 or placement by the Department of Mathematics.

090. Mathematics Refresher (3 sem. hrs.). This course is designed to review topics from arithmetic and elementary algebra. It is the goal of this course to prepare the student who comes to Heidelberg with mathematics deficiencies to enter MTH 115, Quantitative Reasoning. Major emphasis will be given to applications in business, the natural sciences and the social sciences. This course does not fulfill any degree requirements of any major. A student taking this course will need an additional three hours to graduate. Placement into this course will be determined by placement testing and evaluation of high school transcript. (Fall and Spring)

115. Quantitative Reasoning (3 sem. hrs.). This course will cover a broad range of topics with emphasis given to applications in business, the natural sciences and the social sciences. Topics include the basics of set theory, functions, systems of linear equations and inequalities, linear programming, permutations, combinations, probability and descriptive statistics. It is a goal of this course to improve skills in problem solving and the ability to think quantitatively. This course does not fulfill any requirements of the mathematics major. Prerequisite: Recommendation of the Mathematics Department or successful completion (C- or better) of MTH 090. (Fall and Spring)

117. Mathematics for Elementary Education I (3 sem. hrs.). Topics covered are set theory, numeration systems, estimation, number theory, counting procedures (permutations and combinations), geometry and measurement. Problem solving, communication skills and critical thinking will be emphasized in the treatment of all topics. This course does not fulfill any requirements of the mathematics major, or General Education Requirements. Prerequisites: Completion of (or current enrollment in) EDU 200 and successful completion of MTH 090 (C- or better) or placement by the Mathematics Department. (Fall)

118. Mathematics for Elementary Education II (3 sem. hrs.). Topics covered are the study of the real numbers including integers, rational numbers, decimals and percents with applications; analytic geometry; probability and statistics. Problem solving, communication skills and critical thinking will be emphasized in the treatment of all topics. This course does not fulfill any requirements of the mathematics major. Prerequisite: MTH 117. (Spring)

121. Elementary Functions (3 sem. hrs.). Study of elementary functions, their graphs and applications, including polynomials, rational functions, algebraic functions, exponential, logarithmic and trigonometric functions and plane analytic geometry. This course does not fulfill any requirements of the mathematics major, nor does it fulfill the prerequisite requirement for MTH 210. Prerequisite: Recommendation of the Mathematics Department, or MTH 115. (Fall and Spring)

210. Elementary Statistics (3 sem. hrs.). The purpose of this course is to introduce the student to statistical methods and techniques with emphasis given to applications in business, the natural sciences, psychology, and the social sciences. Topics include probability distributions, hypothesis testing (large and small sample), Chi-Square test, ANOVA, correlation and regression and nonparametric testing. This course does not fulfill any requirements of the mathematics major. Prerequisite: MTH 115 or 118. (Fall and Spring)

222. Calculus I (3 sem. hrs.). The development of the concepts of limit, continuity and derivatives, and the associated computational techniques. Applications to the study of motion, optimization, and related concepts in other areas of the natural and social sciences are included. Prerequisite: Placement or MTH 121. (Fall and Spring)

223. Calculus II (3 sem. hrs.). The development of the concepts of the definite and indefinite integral, the fundamental theorem of calculus, applications to area, volume and related physical concepts, use of integrals to extend our knowledge of the transcendental functions: logarithmic, exponential and inverse trigonometric functions. Prerequisite: MTH 222. (Fall and Spring)

302. Ordinary Differential Equations (3 sem. hrs.). Solutions of differential equations of the first order and first degree, singular solutions, linear differential equations, integration in series, systems of equations and Laplace transforms. Prerequisite: MTH 223. (Fall of odd-even years)

303. Linear Algebra (3 sem. hrs.). Finite-dimensional vector spaces, matrix theory, linear transformations, systems of linear equations and quadratic forms. Prerequisite: MTH 222. (Spring of odd-even years)

305. College Geometry I (3 sem. hrs.). A study of finite geometries and graph theory, the axiomatic development of Euclidean geometry, and a brief introduction to non-Euclidean geometry. The course also presents the history of the development of both Euclidean and non-Euclidean geometry. Prerequisite: MTH 223. (Spring of odd-even years)

306. College Geometry II (3 sem. hrs.). A study of non-Euclidean geometry which includes projective and hyperbolic geometry. Prerequisite: MTH 305. (Offered on demand)

307. Calculus III (3 sem. hrs.). Advanced techniques of integration, sequences and series, parametric and polar coordinates, vector and analytic geometry of three dimensions. Prerequisite: MTH 223. (Fall only)

308. Calculus IV (3 sem. hrs.). Vector-valued functions and curves in 3-space, functions of several variables and partial derivatives, multiple integrals and applications. If time allows, additional topics in vector analysis will be covered. Prerequisite: MTH 307. (Spring only)

310. Introduction to Numerical Analysis (3 sem. hrs.). An introduction to the computer techniques and algorithms used to solve numerical problems. Number representation, roots of nonlinear equations, numerical integration, linear systems, numerical solution of differential equations, Monte Carlo methods, simulation and curve fitting. Prerequisites: MTH 307 and CPS 201. (Fall of even-odd years)

312. Introduction to Mathematical Statistics (3 sem. hrs.). Probability theory; moments; binomial, normal, t, Poisson and Chi square distributions; random sampling; hypothesis testing and non-parametric tests. Prerequisite: MTH 223. (Spring of even-odd years)

321, 322. Independent Study (2 sem. hrs.). Open to juniors or seniors of proven ability. Topics chosen from the field of analysis, algebra, topology, geometry or number theory according to a student’s interest. A maximum of four hours is permitted. (Offered on demand)

390. Mathematical Communication Skills (1 sem. hr.). This course will complete the general education requirement for junior-level written and oral communications within the mathematics department. Students will learn to use appropriate terminology and notation in writing and speaking about mathematical ideas, proofs, and journal articles. Students will be required to attend a talk outside of scheduled class hours. Prerequisite: Must be taken concurrently with MTH 302, 303, 305, 308, or 312. Open to juniors and seniors. (Offered on demand)

401. Abstract Algebra (3 sem. hrs.). Introduction to the concepts of modern algebra, particularly those of group, ring, integral domain and field. Includes applications to number theory. Prerequisite: MTH 308. (Spring of even-odd years)

402. Topology (3 sem. hrs.). An introduction to point set topology, topological and metric spaces and their properties. Prerequisite: MTH 308. (Fall of odd-even years)

403. Complex Analysis (3 sem. hrs.). Algebra and geometry of complex numbers and analytic functions. Cauchy’s theorem and formula, contour integration and conformal mapping. Prerequisite: MTH 308. (Spring of odd-even years)

404. Real Analysis (3 sem. hrs.). Introduction to real variable theory; construction and completeness of the real numbers; set theory; continuity, differentiability and measurability. Prerequisite: MTH 308. (Fall of even-odd years)

475, 476. Honors Course (3 sem. hrs.). (Offered on demand)

490. Math Capstone (1 sem. hr.). This course will satisfy the capstone requirement for the math major. Students will conduct a research project on an instructor’s approved topic and present results in written and oral form. Co-requisite: MTH 401, 402, 403, or 404. Open to juniors and seniors. (Offered on demand)