Mathematics Requirements
Requirements for a major in mathematics: Mathematics 206, 224, 500 and four mathematics courses numbered at the 200 level or above (excluding 401), of which at least one must be at the 300 level and at least one at the 400 level. Students intending to study mathematics in graduate school should speak to their advisers about appropriate courses.
Requirements for a minor in mathematics: Eighteen credits in mathematics courses (excluding 401) together with a capstone experience. A coherent program of courses must be designed in consultation with a member of the department and approved by the department. The capstone experience could be a course in any department, an independent study course or an internship. The student will successfully present a talk based on the capstone experience to the senior seminar.
Requirements for a teaching major in mathematics: Mathematics 130, 141-142, 206, 224, 261, either 120 or 432, 303, 401, 422, 500; and Computer Science 110.
Requirements for a teaching minor in mathematics: Mathematics 130, 141-142, 224, either 261 or 422, 401; and Computer Science 110.
The department conducts a colloquium series. These meetings are open to all students; majors are expected to attend.
Mathematical Thinking and Writing [Mathematics 130 (with a special version, Mathematics 133, Applications of Calculus)] is our introduction to the discipline of mathematics. As such, it is the course that would normally be taken by students who are beginning their study of mathematics at Ripon College. But there are exceptions:
1) Students who do not plan to study mathematics at the calculus level or higher. These
students also would be well-served by Finite Mathematics (Mathematics 123) or
Elementary Statistics (Mathematics 120);
2) Students who plan to study mathematics at the calculus level or higher but whose high school background is weak. Typically, these would be students who have not successfully completed high school mathematics courses through the traditional fourth-year level. (This would be a course that goes by a variety of names, including Precalculus, Functions, Math Analysis and Math 4. It should include a study of trigonometry, analytic geometry and functions. Calculus is not required,) These students probably would do better to start in Finite Mathematics (Mathematics 123). If their performance in Finite Mathematics warrants it, the instructor may recommend to the department that Mathematical Thinking and Writing be waived.
3) Students who have received college credit for a course equivalent to Calculus I. (This exception does not apply to students who have taken a high school course in calculus but did not receive college credit.) If they prefer not to interrupt their study of calculus, they may go directly to Calculus II (Mathematics 142). But afterwards they will need to take Mathematical Thinking and Writing before they study more advanced courses.
4) There may be a rare student who, by virtue of a rich mathematics background, has achieved the objectives of Mathematical Thinking and Writing. Such a student should consult with a member of the department about the possibility of advanced placement and waiver of the Mathematics 130 requirement.
Departmental assistants are available to help tutor students with deficiencies in mathematics.
All prerequisites for mathematics courses must be passed with a grade of C- or better.
Courses
120. Elementary Statistics (D. Beres, K. Beres, Loomer)
Four credits. Descriptive and inferential statistics. Topics include probability distributions and sampling distributions, regression and correlation, point estimates and confidence intervals, and hypothesis
testing.
123. Finite Mathematics (Staff)
Four credits. An introductory course in discrete mathematics.
Topics selected from combinatorics, probability, matrices, linear
programming, Markov chains, graph theory and other applications.
Applications to the life sciences, social sciences and computer
science.
130. Mathematical Thinking and Writing (K. Beres,
Loomer, Scott)
Four credits. An introduction to mathematics through the
study of the history of mathematics, with special emphasis on the
development of students' problem-solving and communication skills.
133. Applications of Calculus (K. Beres)
Four credits. An introduction to mathematics through the
study of applications of calculus, with special emphasis on the development
of students' problem-solving and communication skills. This course
is a version of Mathematics 130 intended for students who have had
an exposure to calculus before coming to Ripon College. Normally,
students who complete Mathematics 133 would take Mathematics 142,
Calculus II; they would not be permitted to earn credit for both
Mathematics 133 and 141, Calculus I.
141-142. Calculus I and II (Staff)
Four credits each semester. Analysis of the elementary functions
of a single variable including differentiation and integration, techniques
of integration, theory of limits, infinite series, applications. Prerequisite for Mathematics 141: Mathematics 123 (with the recommendation of the instructor) or Mathematics 130, or consent of the department. Prerequisite for Mathematics 142: Mathematics 130 and 141, or Mathematics 133, or the consent of the department.
146. Computer Modeling (K. Beres)
Four credits. An introduction to computer simulations and the use of computer models as an aid to decision-making. Examples will be drawn from a variety of disciplines. Students will explore and create models using various software, such as spreadsheets and GIS. Students will work on projects both individually and in small groups. Prerequisite: Consent of the instructor.
206. Multiple Variable Calculus (Staff)
Four credits. Calculus of functions of several variables;
parametric equations; polar coordinates; applications. Prerequisites: Mathematics 130 or 133, and Mathematics 142 or its equivalent; or the consent of the department.
220. Data Analysis (Loomer)
Four credits. An integrated treatment of statistical procedures
as tools for building and testing models of data. Topics include
regression, correlation, analysis of variance and analysis of covariance. Prerequisite:
Mathematics 120.
224. Linear Algebra (Staff)
Four credits. Matrices, vectors, determinants, vector spaces,
linear transformations and applications. Prerequisite: Mathematics
130 or 133, 142 or its equivalent, or the consent of the department.
246. Mathematical Modeling (K. Beres)
Four credits. Offered in 2008-09 and alternate years. An introduction to applied mathematics. Topics chosen by the instructor. With permission of the instructor, this course may be repeated for credit as 346 and 446. Prerequisites: One semester of calculus.
248. Discrete Mathematics (Staff)
Four credits. Topics chosen from set theory, combinatorics,
recurrence relations, graph theory, Boolean algebra, applications.
Same as Computer Science 248. Prerequisite: Mathematics 123 or
130 or 133. Familiarity with a programming language is desirable.
261. Geometry (Scott)
Four credits. Offered in 2007-08 and alternate years. Topics from modern Euclidean geometry, transformations, projective geometry and non-Euclidean geometry. Prerequisite: Mathematics 130, 133, or the consent of the department.
290. Modeling Club (Staff)
Two credits. Continuous and discrete mathematical models
are studied in preparation for the COMAP Mathematical Contest in
Modeling. May be counted only once towards major or minor requirements.
Grading is S-U.
300. Departmental Studies (Staff)
One to four credits. Special subjects in mathematics not covered by regular courses. Topics are announced as courses are offered. This course may be repeated for credit when topics change. Prerequisite: Consent of the department.
303. Complex Variables (Staff)
Four credits. Offered in 2007-08 and alternate years. Complex numbers, elementary functions, analytic functions, series, integrals, Cauchy’s Integral Formula, mappings, poles and residues. Prerequisites: Mathematics 206 and one higher-numbered mathematics course.
323. Number Theory (Beres)
Four credits. Offered in 2008-09 and alternate years. Properties of primes, congruencies, quadratic residues and Diophantine equations; computer applications. Some experience in programming is helpful. Prerequisites: Mathematics 130 or 133, or the consent of the department.
331. Probability (Staff)
Four credits. Offered in 2007-08 and alternate years. Probability as a mathematical system, combinatorics, random variables and their distributions, limit theorems and applications. Prerequisite: Mathematics 130 or 133, and Mathematics 142 or its equivalent; or the consent of the department.
343. Differential Equations (Staff)
Four credits. Offered in 2008-09 and alternate years. Ordinary differential equations, numerical solutions and applications. Prerequisite: Mathematics 130 or 133, 142 or its equivalent, or the consent of the department.
401. Secondary Teaching Methods (Scott)
Two credits. Offered on demand. Mathematics education methods,
materials and philosophies. Prerequisite: Consent of the department.
405. Real Analysis
Four credits. Offered in 2008-09 and alternate years. The real numbers, metric concepts and continuity, differentiation and integration of real functions, infinite sequences and series of functions. Prerequisites: Mathematics 206 and one higher numbered mathematics course.
412. Topology (Loomer, Scott)
Four credits. Offered in 2005-06 and alternate years. An
introduction to topology, including topological spaces, connectedness,
compactness, countability and separation axioms, and metric spaces. Prerequisite:
Consent of the department.
422. Algebraic Structures (Staff)
Four credits. Offered in 2005-06 and alternate years. Groups,
homomorphisms, isomorphisms, factor groups, rings, fields and polynomials. Prerequisite:
Mathematics 224 and one higher-numbered mathematics course.
432. Mathematical Statistics (Loomer)
Four credits. Correlation and regression, sampling and estimation
theory, testing hypotheses and applications. Prerequisites:
Mathematics 206 and 231.
500. Senior Seminar (Staff)
One-year course. Two credits. Selected topics presented by students. Same as Computer Science 500. Required of senior majors; open to others by consent of the department. Prerequisite: senior standing and one course in the department at the 300 level or higher, or consent of the department.
540. Independent Study (Staff)
One to four credits. Supervised investigation of problems
in mathematics of special interest to the student. Prerequisites:
Junior or senior standing, 12 credits toward the major and consent
of the department.
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