Next: Medieval and Early Modern
Up: Courses of Instruction
Previous: Latin American Studies (LAS)
Mathematics (MAT)
Stephen Bean, Ann Cannon, Tony deLaubenfels,
James Freeman (chair)
Major: 10-12 course credits. Completion of the calculus sequence (through MAT 122); a minimum of seven Mathematics courses at the 200- or 300-level which include MAT 221, 236, 301, either 327 or 337, and two additional courses at the 300-level; CSC 151, 140; and INT 201 (if MAT 348 is not one of the 300-level courses completed). The department recommends that CSC 140, which provides knowledge of a programming language, be acquired by the end of the sophomore year. The following courses cannot be used to satisfy requirements of the mathematics major: MAT 110, 280/380, 290/390, 501, and 511.
Teaching Major:
Completion of the requirements for the Mathematics major with the additional stipulations that MAT 231 is required to be one of the seven Mathematics courses and that the grade point average in all Mathematics courses must be at least 2.5. In addition to the foregoing requirements, prospective teachers must also apply for admission to the Teacher Education Program (preferably at the start of their sophomore year) and complete a second major in Secondary Education described under Education.
Second Teaching Area in Mathematics: The following program, in conjunction with a teaching major in another field, will enable the student to apply for licensure to teach both the major subject and Mathematics: MAT 231, either 327 or 337, either INT 201 or MAT 348, and have a grade point average in all Mathematics courses of at least 2.5.
Minor: Five or six credits. Completion of the calculus sequence (through MAT 122); a minimum of three Mathematics courses which include MAT 221, 301, and at least one other 300-level Mathematics course; and CSC 151.
110. On the Shoulders of Giants: Great Mathematical Ideas
Investigation of a variety of great mathematical discoveries past and present. The ideas investigated will not require significant previous mathematical background, but will require the student to actively participate in the process of mathematical discovery. Only by doing mathematics can the creativity, beauty, and mathematical importance of these great ideas be understood. Specific content varies with the course instructor, but may include subjects such as knot theory, origami, game theory, the nature of infinity, or chaos and fractals. Prerequisite: two years of high school algebra. Recommended for non-mathematics majors. This course is not open to students who have completed MAT 120 or higher. This course does not count toward a mathematics major or minor. (Mathematics) BEAN or J.FREEMAN
119-120. Calculus of a Single Variable Part I & II
Differential and integral calculus of functions of one real variable and analytic geometry of two variables. This course emphasizes review of precalculus material and is appropriate for students who feel they need more time in order to succeed in calculus. Prerequisite: Three and one-half years of high school mathematics, including trigonometry. This course is not open to students who have completed MAT 121 or higher. (Mathematics)
121. Calculus of a Single Variable
Differential and integral calculus of functions of one real variable and analytic geometry of two variables. Prerequisite: Three and one-half years of high school mathematics, including trigonometry, in addition to ACT Math score of 25 or above, or SAT Math score of 570 or above, or permission of instructor. This course is not open to students who have completed MAT 120. (Mathematics)
122. Calculus of Several Variables
Continuation of Calculus of a Single Variable, including further techniques of integration, vectors, and differential and integral calculus of several variables. Prerequisite: MAT 120 or 121.
221. Linear Algebra
Existence and uniqueness of solutions to linear systems. Linear transformations, linear independence, spanning vectors, vector spaces, basis and dimension, orthogonality, eigenvalues and eigenvectors. Students will be required to prepare written and oral presentations on a linear algebra application approved by the instructor. Prerequisites: either MAT 120 or 121 and either CSC 151 or MAT 122.
231. Fundamentals of Geometries
An examination of the assumptions inherent in the axiomatic structures of two-dimensional geometry through the parallel postulate and its alternatives. Additional topics may include projective geometries, finite geometries, coordinates and transformations, tilings, and higher-dimensional objects. Prerequisite: MAT 221. Alternate years. BEAN
234. Complex Variables
Differential and integral calculus of functions of one complex variable. Analytic and harmonic functions, contour integration, Laurent series, residue theory, and conformal mapping. Prerequisite: MAT 122. Alternate years.
236. Differential Equations
This course is about how to predict the future. Mathematical modeling with differential equations, initial value problems and their approximate solutions, systems of differential equations, qualitative solutions, stability analysis and an introduction to chaos, and Laplace transforms. Prerequisites: MAT 122 and 221. CANDELARIA
255 through 260. Topics in Mathematics
A topic of mathematics more computationally oriented than proof oriented. Prerequisite: MAT 122 and/or 221.
301. Introduction to Proof: Number Theory
An introduction--through the subject of number theory--to the ideas, logic, techniques, and reasoning used in writing a mathematical proof. Divisibility and factorization properties of integers, congruences, prime numbers, Diophantine equations, Fermat's Theorem, Wilson's Theorem, and Euler's Theorem, and applications. Prerequisites: CSC 151 and MAT 221.
317. Mathematical Modeling
An introduction to the process and techniques of modeling using tools from linear algebra, differential equations, and other mathematical disciplines. Appropriate mathematics and computational technology, including numerical methods, developed as needed. Models drawn from the physical sciences, life sciences, social sciences, and computing, with extensive use of case studies. Prerequisites: CSC 140 and MAT 236. Alternate years. CANDELARIA
327-328. Modern Algebra I & II
Formal systems of algebra (groups, rings, integral domains, and fields) and their relations to other disciplines. Prerequisite: MAT 301. Alternate years. J.FREEMAN
337-338. Analysis I & II
Topics from the theory of functions of a real variable. First term will include limits and continuity, differentiation and theories of integration. Second term will extend these results to sequences and series of functions. The second term will include student reading projects and presentations on theory and/or applications related to analysis topics. Prerequisites: MAT 122 and 301. Alternate years. BEAN
347-348. Mathematical Statistics I & II
Typically the first term covers probability, random variables, sampling distributions and collecting data. The second term covers theory of estimation and hypothesis testing, linear and multiple regression, analysis of variance, and techniques for categorical data. The second term also includes a substantial data analysis project including written and verbal presentations. Prerequisites: MAT 122 and 301. Alternate years. CANNON
355 through 360. Advanced Topics in Mathematics
A proof oriented topic in mathematics. Prerequisite: MAT 301.
380. Internship: see Courses 280/380.
390. Individual Project: see Courses 290/390.
501. Problem Solving (1/4)
Weekly participation in problem solving. To receive credit the student must participate in a recognized undergraduate mathematics competition, such as the Iowa Collegiate Mathematics or Putnam Competitions. Must be taken over four consecutive terms. No more than one credit of MAT 501 can be earned.
511. Extended Research in Mathematics (1/4)
Developing and proving statements in an interesting area of mathematics which are original to the student. Must be taken over four consecutive terms. Prerequisites: CSC 151, MAT 122, a GPA in the department of 3.0 or higher and permission of instructor. No more than one credit of MAT 511 can be earned.
541. Intermediate Calculus (1/4)
A course to address differences in the curriculums of the old MAT 141 and the new MAT 121, namely the definition of the definite integral, the Fundamental Theorem of Calculus, and integration by substitution. Prerequisite: MAT 141.
|
