Note: This page is intended to provide an accurate reproduction of the information in the Hope College 2007-08 Catalog. Please see the Catalog for Hope College policies relating to changes in this information. Unless otherwise indicated, the terms Fall Semester and Spring Semester refer to Fall 2007 and Spring 2008, respectively.

123. A Study of Functions:
A study of functions including polynomial, rational, exponential, logarithmic, and trigonometric functions. These will be explored in their symbolic, numerical, and graphic representations, and connections between each of these representations will be made. A graphing calculator is required. A student cannot receive credit for both MA 123 and MA 125. Four Credits, Spring Semester

125. Calculus with Review I:
This course covers the material typically taught in the first half of a Calculus I (MA 131) course. The calculus material is supplemented by reviewing topics of high school mathematics as needed. The calculus topics are also taught at a slower pace. Topics include function review, limits and continuity, the concept (and definition) of a derivative, and differentiation rules (product rule, quotient rule, and chain rule are included). A student cannot receive credit for both MA 123 and MA 125. Four Credits, Fall Semester

126. Calculus with Review II:
This course is a continuation of MA 125. The topics covered are the topics typically taught in the second half of a Calculus I (MA 131) course. The calculus material in the course is supplemented by reviewing topics of high school mathematics as needed. The calculus topics are also taught at a slower pace. Topics include implicit differentiation, applications of differentiation, L'Hospital's rule, Newton's method, the integral, and applications of integration. Prerequisite: completion of Math 125 with a grade of C- or better, or permission of instructor. A student cannot receive credit for both MA 126 and MA 131. Four Credits, Spring Semester

131. Calculus I:
Topics include functions, limits, continuity, differentiation, integration and applications of the derivative and integral. A student cannot receive credit for both MA 126 and MA 131. Four Credits, Both Semesters

132. Calculus II:
Topics covered include techniques of integration, applications of integration, sequences, infinite series, power series, introduction to differential equations, and polar coordinates. Prerequisite: completion of MA 126 or MA 131 with a grade of C- or better, or permission of instructor. Four Credits, Both Semesters

205. Mathematics for Elementary Teachers I:
A course sequence in mathematics content designed to explore fundamental aspects of the mathematics encountered in grades K-8. First semester topics include patterns, problem solving, sets, geometry, operations with whole numbers, and rational and real numbers. For prospective elementary teachers only. Four Credits, Fall Semester

206. Mathematics for Elementary Teachers II:
A continuation of MA 205. Topics include measurement, statistics, and probability. For prospective elementary teachers only. Prerequisite: MA 205 or permission of the instructor. Two Credits, Spring Semester

207. K-8 Mathematics Software Applications:
A course designed to deepen understanding of mathematical concepts by exploring several available software packages, including LOGO. For prospective elementary teachers only. Prerequisite: completion of MA 205 or permission of instructor. Two Credits (Next offered Spring 2009)

208. Problem Solving for Elementary Teachers:
A course designed to integrate content areas of mathematics with the practice of problem solving. Emphasis will be given to group work, oral presentation and multiple solution methods. For prospective elementary teachers only. Prerequisite: completion of MA 205 or permission of instructor. Two Credits, Spring Semester

210. Introductory Statistics:
Activities and projects are used to motivate and illustrate statistical concepts. Data collected by students are integrated into this course. Data are examined visually and numerically. Correlation and regression are used to determine relationships in paired data. The binomial and normal distributions are included. Estimation, confidence intervals, and test hypotheses are studied. A statistical software package and a statistical calculator are used. This is a general introduction to descriptive and inferential statistics. Four Credits, Both Semesters

231. Multivariable Mathematics I:
The study of linear algebra and ordinary differential equations. Prerequisite: completion of MA 132 with a grade C- or better, or permission of instructor. Four Credits, Both Semesters

232. Multivariable Mathematics II:
The study of systems of differential equations and multivariable calculus including differentiation, multiple integration, and calculus on vector fields. Prerequisite: completion of MA 231 with a grade of C- or better, or permission of instructor. Four Credits, Both Semesters

280. Bridge to Higher Mathematics - An Introduction to Mathematical Proof:
An introduction to the understanding and creation of rigorous mathematical argument and proof. Topics include properties of the integers, real numbers, and integers modulo n. Additional topics may include mathematical induction, elementary set theory, elementary number theory, recursion formulas, counting techniques, equivalence relations, partitions, and cardinality of sets. There will be a heavy emphasis on writing, in particular the writing of mathematical arguments and proofs. Prerequisite: MA 132. Two Credits, Spring Semester

295. Studies in Mathematics:
A course offered in response to student interest and need. Covers mathematical topics not included in regular courses. Prerequisite: permission of instructor or department chairperson. One, Two or Three Credits, Both Semesters

310. Statistics For Scientists:
This course is no longer in the Hope College Catalog. It has been replaced by the Math 311-312 sequence.

311. Statistical Methods:
A first course in statistical methods, this course covers the basics of descriptive and inferential statistics. Course topics include numerical and graphical descriptive techniques, confidence intervals, hypothesis testing and simple linear regression. Prerequisite: MA 132. Two Credits, Spring Semester

312. Applied Statistical Models:
This course provides a survey of statistical methods students would expect to see utilized across disciplines in peer reviewed research. Topics include multiple and non-linear regression, non-parametric methods, general linear models, and multivariate statistical models. Students will learn by way of case studies on real data. Prerequisite: MA 210 or 311. Two Credits, Spring Semester

321. History of Mathematics:
This course is designed to give mathematics students an opportunity to study the various periods of mathematical development. Attention will be given to the early Egyptians-Babylonian period, the geometry of Greek mathematicians, the Hindu and Arabian contribution, the evolution of analytical geometry since Decartes, the development of calculus by Newton and Leibniz, and non-Euclidean geometry. Some attention will be given to the methods and symbolism used in problem solving during various periods of time. Prerequisite: MA 132. Two Credits, Fall Semester

323. Teaching of Mathematics In The High School:
Methods of teaching mathematics with emphasis on varied approaches, classroom materials, curriculum changes, and trends in mathematics education. Same as Educ. 323. Prerequisite: admission to the Teacher Education Program. Two Credits, Fall Semester

331. Advanced Calculus I:
Study of the real number system, sequences, functions, continuity, uniform continuity, differentiation, and the theory of integration. Prerequisite: MA 232 and MA 280. Three Credits, Fall Semester

332. Advanced Calculus II:
A continuation of MA 331 including functions of several variables, series, uniform convergence, and Fourier series. Prerequisite: MA 331. Three Credits, Spring Semester When Offered

334. Complex Analysis:
The study of the algebra and geometry of complex numbers, analytic functions, complex integration, series, and conformal mapping. Prerequisite: MA 232 or permission of instructor. Three Credits, Spring Semester

341. Algebraic Structures I:
An introduction to algebraic systems including a study of groups, rings, and integral domains. Prerequisite: MA 232 and MA 280. Three Credits, Fall Semester

342. Algebraic Structures II:
A continuation of MA 341 including a study of topics in fields, Galois theory, and advanced linear algebra. Prerequisite: MA 341. Three Credits, Spring Semester When Offered

345. Linear Algebra:
The study of abstract vector spaces, matrices and linear transformations, determinants, canonical forms, the Hamilton-Cayley theorem, inner product spaces. Prerequisite: MA 232. Three Credits, Spring Semester

351. College Geometry:
A modern approach to geometry for students with some background in calculus and an interest in secondary teaching. Attention is given to the role of axioms in elementary geometry and in the development of other geometries. Prerequisite: MA 231 or permission of instructor. Three Credits, Fall Semester

370. Advanced Differential Equations:
Advanced topics in ordinary differential equations, including series solutions and orthonormal sets of solutions. Introduction to partial differential equations including the heat equation, the wave equation, and the potential equation. Boundary value problems and Fourier Series will also be covered. Three Credits, Not Offered 2007-08

372. Numerical Analysis:
The study of the source and analysis of computational error, finding the solution of an equation, systems of linear equations, interpolation and approximation, and numerical integration. Prerequisites: Computer Science 120 and MA 232. Three Credits, Not Offered 2007-08

375. Operations Research:
Decision making using mathematical modeling and optimization. Linear programming. Network analysis. Dynamic programming. Game theory. Queuing theory. Computer programs may be written to implement these techniques. Prerequisites: MA 232. Three Credits

434. Elementary Topology:
A systematic survey of the standard topics of general topology with emphasis on the space of real numbers. Includes set theory, topological spaces, metric spaces, compactness, connectedness, and product spaces. Prerequisite or corequisite: MA 331. Three Credits

490. Independent Study And Research:
Course provides opportunity for a junior or senior mathematics major to engage in an independent study project or a research project in an area of mathematics in which the student has special interest. Prerequisite: Permission of the chairperson of the department. One, Two, or Three Credits, Both Semesters

495. Advanced Studies In Mathematics:
Offered as needed to cover topics not usually included in the other mathematics courses. A student may enroll for either or both semesters. Prerequisite: Permission of the chairperson of the department. One, Two or Three Credits, Both Semesters