Mathematics (MTH)
Professors Molina, Nyman and Putz; Associate Professors Dai and Sipka.
Working within a structured, quantitative framework and thinking abstractly are experiences encountered by all who study the mathematical sciences. Because mathematics is the study of pattern as well as content, its applications span diverse fields.
Students trained in mathematics find employment in actuarial science, computer systems analysis and programming, engineering, industrial research and development, statistical quality control and teaching. Graduates of Alma's Mathematics Programs have entered graduate school in actuarial science, economics, engineering, law, management science, medicine, operations research and statistics.
Mathematics Major
- Thirty-six credits which must include:
- Mathematics 121, 122, 210, 223, 310, and 421 or 431.
- Twelve other upper-level Mathematics credits.
- Two required cognate courses:
- Computer Science 120.
- A course, other than a Mathematics course, approved by the Department, with a Mathematics prerequisite numbered 113 or higher.
- The senior comprehensive examination includes three parts: successful completion of the Major Field Test in Mathematics, submission of an approved writing sample and an approved oral presentation.
- At least one statistics course is recommended.
- Students interested in graduate school in mathematics should complete both Mathematics 421 and 431 and an honors project. Students interested in business and industrial careers should consider additional courses in Applied Mathematics, Computer Science and fields which apply mathematics in significant ways.
Mathematics Minor
Twenty-four credits which must include Mathematics 121, 122, 210 and at least two other upper-level Mathematics courses. (Mathematics 099, 101 and 202 do not count toward the Minor.)
Mathematics Secondary Teaching Major
Same as for the Mathematics major except that the program must include Mathematics 341, 411, and 421.
Mathematics Secondary Teaching Minor
Twenty-six or 28 credits in Mathematics that must include MTH 120, 121, 122, 223, 411; 117 or 310; and 116 or 341.
Mathematics Elementary Teaching Minor
Twenty-four credits which must include Mathematics 110; 116; 120; 113 or 121; and Computer Science 114, 117 or 120 and four additional credits at the MTH 110 level or above. (Mathematics 099, 101 and 202 do not count toward the Elementary Teaching Minor.)
Mathematical Sciences Major
Fifty-two credits which must include Mathematics 121, 122, 210, 223, 310, 336, 341, and 421 or 431; Computer Science 120 and 220, and 12 additional credits in upper-level Mathematics or Computer Science courses, at least four credits of which must be Computer Science. Courses which combine applications and theory are encouraged (e.g. Mathematics 211, 342, 391, 399 or 499; and Computer Science 240, 310, 420, 430, 440, or 499). The senior comprehensive examination includes three parts: successful completion of the Major Field Test in Mathematics, submission of an approved writing sample and an approved oral presentation.
Restrictions
The following combinations of double majors are not permitted: Mathematical Sciences and Mathematics; and Mathematical Sciences and Computer Science.
Four credits from MTH 110 or higher, with the exception of practicum or independent study courses, count towards the Distributive Requirements in the Natural Sciences — Mathematics/Computation.
| MTH 099. | Basic Core Mathematics | |
|---|---|---|
| 4 credits | ||
| Placement | ||
| Designed for students with very weak backgrounds in mathematics. Focuses primarily on skills development, including the arithmetic of real numbers, construction and interpretation of graphs, introduction to linear relationships and simple notations from statistics. Students required to enroll in this course must complete four additional credits for the bachelor's degree. Pass/fail only. | ||
| MTH 101. | Basic Algebra | |
| 4 credits | ||
| MTH 099 or Placement | ||
| Fundamentals of elementary algebra. Includes addition, subtraction and multiplication of polynomials, factoring of polynomials, the quadratic formula, graphing of equations, systems of equations and inequalities. May not be taken for credit by students who have successfully completed Mathematics 112 or a higher course. | ||
| MTH 110. | Liberal Arts Mathematics | |
| 4 credits | ||
| MTH 101 | ||
| Exploration of the beauty, extent and power of mathematics. Specific topics to be selected by the instructor. | ||
| MTH 111. | Mathematics in Art and Nature | |
| 4 credits | ||
| MTH 101 | ||
| Mathematics in the visual and musical arts and the plant and animal worlds. Topics include Fibonacci sequence, the golden section, Archimedean and logarithmic spirals, one- and two-point perspective, tessellations of the plane, and Escher-like constructions. | ||
| MTH 112. | Pre-Calculus | |
| 4 credits | ||
| Placement | ||
| Designed for students with strong high school mathematics backgrounds who plan to include a calculus course (Mathematics 113 or 121) in their programs. Investigates polynomial, rational, exponential, logarithmic and trigonometric functions. Explores the ideas of functions and graphs, with emphasis on concepts and skills central to calculus. May not be taken for credit by students who have successfully completed Mathematics 121, 122 or 210. | ||
| MTH 113. | Brief Calculus | |
| 4 credits | ||
| MTH 112 or placement | ||
| Introduction to differential and integral calculus. Focuses on applications; theory held to a minimum. Examples from business and the natural and social sciences. Background in trigonometry not needed. | ||
| MTH 116. | Elementary Statistics | |
| 4 credits | ||
| MTH 101 | ||
| Introduction to modern elementary statistics and applications. Focuses on statistical reasoning and data analysis. Includes statistical design of experiments, estimation, hypothesis testing, regression, correlation and other selected topics. | ||
| MTH 117. | Introduction to Matrices and Linear Methods | |
| 2 credits | ||
| Placement in MTH 112 or 4 years of High School Math | ||
| Introduction to solving systems of linear equations, linear programming, elementary matrix theory, and the modeling of situations which are linear. Applications from business and natural and social sciences. Note: The content of this course is necessary background for Mathematics 310. | ||
| MTH 120. | Discrete Mathematics | |
| 4 credits | ||
| MTH 112 or Placement or 4 years of High School Math | ||
| Introductory survey of propositional logic, functions, relations, counting methods and graph theory. Discussion of applications to computer science. | ||
| MTH 121-122. | Calculus | |
| 4 credits each | ||
| MTH 112 with "C" or better or 4 years of High School Math | ||
| Introduction to the calculus of one variable. Includes limits and continuity, the derivative and applications, the integral and applications, infinite series and sequences. | ||
| MTH 130. | Beyond the Third Dimension | |
| 4 credits | ||
| Permission | ||
| A reading and writing course about dimensions greater than three with emphasis on Euclidean four-dimensional space. In addition to a mathematical text, readings include works from other disciplines. The goal is to gain a better understanding of four (or more) dimensions through various ways of thinking, both mathematical and otherwise. | ||
| MTH 180. | Topics in Mathematics | |
| 2-4 credits | ||
| Selected topics of current or historic importance. Prerequisites vary with topics selected. | ||
| MTH 192. | Mathematical Modeling | |
| 4 credits | ||
| MTH 113 or 121 | ||
| Development of various mathematical models used in business, social sciences and biological sciences; uses and limitations of models in practical situations. Some models use calculus and/or the computer. Computer programming not a prerequisite. | ||
| MTH 202. | Mathematics for the Elementary Teacher | |
| 4 credits | ||
| MTH 101 or Placement; Sophomore Standing; EDC Major | ||
| Overview and examination of the mathematical topics in the K-8 curriculum. Includes arithmetic of integers, decimals and fractions; numeration systems; set theory; problem solving; elementary logic, elementary concepts in probability and statistics; elementary concepts in geometry; and an introduction to computing. | ||
| MTH *210. | Multivariable Calculus | |
| 4 credits | ||
| MTH 122 | ||
| Continuation of Math 122. Includes functions of several variables, vectors, vector-valued functions, three-dimensional analytic geometry, partial differentiation and multiple integration. | ||
| MTH *211. | Differential Equation | |
| 4 credits | ||
| MTH 210 | ||
| Techniques and theory of solving ordinary differential equations. Includes series solutions, numerical methods and applications. | ||
| MTH *220. | Mathematical Foundations of Computer Science | |
| 4 credits | ||
| MTH 120 | ||
| Topics in the mathematical foundations of computer science. Includes graph theory, logic, Boolean algebras, languages and automata, and the analysis of algorithms. | ||
| MTH *221. | Introduction to Cryptography | |
| 4 credits | ||
| MTH 122 | ||
| Introduction to the mathematics from several different branches of the subject including number theory, matrix algebra, probability, and statistics, all of which play a role in enciphering and deciphering secret messages. | ||
| MTH *223. | Mathematical Structures | |
 |
4 credits | |
| MTH 120 and CSC 220, or MTH 122 | ||
| Study of predicate logic, proof techniques, set theory, relations, functions, cardinality and various discrete structures. | ||
| MTH *280. | Topics in Mathematics | |
| 2-4 credits | ||
| Selected topics of current or historic importance. Prerequisites vary with topics selected. | ||
| MTH *310. | Linear Algebra | |
| 4 credits | ||
| MTH 210; MTH 117 strongly recommended | ||
| Study of finite-dimensional real vector spaces; kernel, dimension, basis, linear transformations and their matrices, and eigenvalues. | ||
| MTH *323. | Complex Analysis | |
| 4 credits | ||
| MTH 210 | ||
| Introduction to the theory of functions of a single complex variable. Analytic functions, complex series, Cauchy's theorem and conformal mapping. | ||
| MTH *336. | Numerical Analysis | |
| 4 credits | ||
| MTH 122 and CSC 120 | ||
| Analysis and implementation of numerical algorithms for approximating functions, derivatives and integrals, and for solving nonlinear equations, ordinary differential equations and systems of linear equations. Discussion of standard software packages and techniques for writing efficient and reliable mathematical software in Pascal and/or FORTRAN. | ||
| MTH *341-*342. | Probability and Statistics | |
| 4 credits each | ||
| MTH 122 for 341; MTH 341 for 342 | ||
| Introduction to mathematical theory of probability and statistical inference. Includes data analysis and presentation, discrete and continuous probability models, random variables, mathematical expectation, generating functions, estimation, hypothesis testing, sampling distributions, regression, correlation, time series and other selected topics. | ||
| MTH *351. | Elementary Number Theory | |
| 4 credits | ||
| MTH 223 | ||
| Study of integers, including divisibility, the theory of prime numbers, congruences and solutions of equations in integers. | ||
| MTH *380. | Topics in Mathematics | |
| 4 credits | ||
| Selected topics of current or historic importance. Background prerequisites vary with topics. | ||
| MTH *390. | Combinatorics | |
| 4 credits | ||
| MTH 120 or 122 | ||
| Introduction to combinational theory. Topics include enumeration, recurrence, generating functions, graph theory and optimization. | ||
| MTH *391. | Introduction to Graph Theory | |
| 4 credits | ||
| MTH 122 or Permission | ||
| Introductory survey of the major concepts and applications of graphs, digraphs and networks. Application areas include transportation, traffic flow, games and puzzles. | ||
| MTH *399. | Independent Study | |
| 1-4 credits | ||
| Permission | ||
| MTH *411. | College Geometry | |
| 4 credits | ||
| MTH 223 | ||
| Axiomatic systems, models, finite geometries, Hilbert's axioms, independence of the parallel postulate, and introduction to non-Euclidean geometries with emphasis on hyperbolic geometry. | ||
| MTH *413. | Topology | |
| 4 credits | ||
| MTH 223 | ||
| Introduction to point-set topology. Includes topological properties of Euclidean spaces, abstract spaces and metric spaces. Explores connectedness, compactness, continuity and homeomorphisms. | ||
| MTH *421. | Abstract Algebra | |
| 4 credits | ||
| MTH 223 and 310 | ||
| Introduction to the theory of algebraic structures including elementary theory of groups, rings and fields. | ||
| MTH *431. | Advanced Calculus | |
| 4 credits | ||
| MTH 210 and 223 | ||
| In-depth examination of the calculus of one variable, including topology of the real line, sequences and series of functions. | ||
| MTH *491. | Mathematical Methods of Physics | |
| 4 credits | ||
| MTH 211; MTH 310 recommended | ||
| Survey of advanced mathematical topics for application in the physical sciences. Topics selected from Fourier series, transform calculus, partial differential equations, boundary value problems, complex variables and vector calculus. Highly recommended for students planning graduate study in the physical sciences or applied mathematics. | ||
| MTH *499. | Independent Study | |
| 1-4 credits | ||
| Permission | ||
| MTH *500. | Senior Thesis | |
|
4 credits | |
| Permission | ||