Course Listings — Fall 2004

MATH 112 THE LANGUAGE OF MATHEMATICS
4 SEM HRS
BARHORST

This is an introduction to mathematics at the beginning college level. MATH 112 will explore topics in contemporary mathematics with a problem-solving approach.

The class meetings will include lectures, problem-solving sessions, and group work. The final grade will be based on quizzes, exams, a project, and/or a comprehensive final. The prerequisite for this course is Math Placement Level 22 or higher. This course is not intended to prepare students for further courses in mathematics. Mathematical-reasoning intensive.

MATH 118 MATHEMATICS FOR ELEMENTARY
4 SEM HRS
KRAUS
AND MIDDLE SCHOOL TEACHERS

Study of number systems, number theory, patterns, functions, measurement, algebra, logic, probability, and statistics with a special emphasis on the processes of mathematics: problem solving, reasoning, communicating mathematically, and making connections within mathematics and between mathematics and other areas. Open only to students intending to major in education. Prerequisite: Math Placement Level 22 or higher. Every year. Mathematical-reasoning intensive.

MATH 119 GEOMETRY WITH LOGO PROGRAMMING
2 SEM HRS
KRAUS
FOR ELEMENTARY AND MIDDLE SCHOOL TEACHERS

Study of basic concepts of plane and solid geometry, including topics from Euclidean, transformational, and projective geometry. Includes computer programming experiences using Logo with a special emphasis on geometry and problem solving. Prerequisites: MATH 118. Every year. Mathematical-reasoning intensive.

MATH 120 ELEMENTARY FUNCTIONS
4 SEM HRS
HODEL

This is a standard pre-calculus mathematics course that explores the functions common to the study of calculus. Examination of polynomial, rational, exponential, logarithmic, and trigonometric functions will be done using algebraic, numeric, and graphical techniques. Applications of these functions in formulating and solving real-world problems will also be discussed.

The final grade in the course is based on quizzes, tests, and a comprehensive final exam. Students are required to have a TI-83, TI-83 Plus, or TI-86 graphing calculator for use in class and for homework assignments.

The prerequisite for this course is Math Placement Level 24 or higher. Mathematical-reasoning intensive.

MATH 127 INTRODUCTORY STATISTICS
4 SEM HRS
ANDREWS

A study of statistics as the science of using data to glean insight into real-world problems. Includes graphical and numerical methods for describing and summarizing data, sampling procedures and experimental design, inferences about the real-world processes that underlie the data, and student projects for collecting and analyzing data. Open to non-majors only.

Prerequisites: Math Placement Level 23 or higher (Note: A student may receive credit for only one of the following statistics courses: MATH 127, MATH 227, PSYC 107, or MGT 210). Mathematical-reasoning intensive.

MATH 131 ESSENTIALS OF CALCULUS
4 SEM HRS
TIFFANY

This one semester calculus course is an introduction to the techniques and applications of differential and integral calculus. The applications come primarily from the bio-sciences and do not involve any trigonometric models. The final grade in the course will be based on quizzes, tests, and a comprehensive final exam.

The prerequisite is MATH 120 or Math Placement Level 25. Students are required to have a TI-83, TI-83 Plus, or TI-86 graphing calculator for use in class and for homework assignments. Mathematical-reasoning intensive.

Notes:

1. Students may not receive credit for both MATH 131 and MATH 201
2. MATH 131 does not satisfy the prerequisite for MATH 202.
3. Take MATH 131 only if you are POSITIVE that you will take only one semester of calculus at Wittenberg. Otherwise, you should take MATH 201.

Calculus is the mathematical tool used to analyze changes in physical quantities. This is the first course in the standard calculus sequence. It develops the notion of "derivative", which is used for studying rates of change, and then introduces the concept of "definite integral", which is related to area problems. The overall approach will emphasize the concepts of calculus using graphical, numerical, and symbolic methods.

The two-semester calculus sequence, MATH 201/202, is required for all students majoring or minoring in mathematics, computer science, physics, or chemistry. MATH 201 and MATH 202 can also count as “supporting science” courses for the BA and BS programs in Biology, Geology, and Biochemistry/Molecular Biology. Students who are sure they will take only one semester of calculus may be better served in the single-semester introduction to calculus, MATH 131: “Essentials of Calculus”. Talk with your advisor or with any math professor for advice on which calculus course is most appropriate for you.

Students are required to have a TI-83, TI-83 Plus, or TI-86 graphing calculator for use in class, for homework assignments, and for tests. If you have a different calculator that you’d like to use for the class, contact the instructor to find out whether your calculator is appropriate.

Depending on the instructor, the final grade in the course could be based on homework, quizzes, tests, and a comprehensive final exam. The prerequisite for the course is MATH 120 or Math Placement Level 25. Mathematical-reasoning intensive.

NOTE: Students may not receive credit for both MATH 131 and MATH 201.

MATH 202 CALCULUS II
4 SEM HRS
HIGGINS

This is the second course in Wittenberg’s three semester calculus sequence. MATH 202 is primarily concerned with integration and power series representations of functions. Topics covered include indefinite and definite integrals, the Fundamental Theorem of Calculus, integration techniques, elementary differential equations, approximations of definite integrals, improper integrals, applications of integrals, power series, Taylor’s Series, geometric series, and convergence tests for series.

Students will be required to have a TI-83, TI-83 Plus, or TI-86 graphing calculator for use in class, for homework assignments, and for tests.

The final grade in the course is based on quizzes, tests, and a comprehensive final exam. MATH 201 is a prerequisite. Mathematical-reasoning intensive.

MATH 205 APPLIED MATRIX ALGEBRA
4 SEM HRS
STICKNEY

A course in matrix algebra and discrete mathematical modeling which considers the formulation of mathematical models, together with analysis of the models and interpretation of the results. Primary emphasis is on those modeling techniques which utilize matrix methods. Such methods are now in wide use in areas such as economic input-output models, population growth models, Markov chains, linear programming, computer graphics, regression, numerical approximation, and linear codes.

Students in this course are required to have a TI-83, TI-83 Plus, or TI-86 graphing calculator for use in class, for homework, and for tests. A TI-89, TI-92, or TI-92 Plus is also acceptable.

This course is a prerequisite for MATH 360 (Linear Algebra), and should be taken by all sophomore mathematics majors. Prerequisites: MATH 201. Mathematical-reasoning intensive.

MATH 215 DIFFERENTIAL EQUATIONS
4 SEM HRS
DAVENPORT

An introduction to elementary ordinary differential equations. Topics covered will include first-order equations, linear equations, nonhomogeneous equations, variation of parameters, linear systems, power series solutions, numerical methods and applications.

The final grade in this course is based on quizzes, tests, a computer project, and a comprehensive final exam. Prerequisite: MATH 202. Mathematical-reasoning intensive.

MATH 227 DATA ANALYSIS
4 SEM HRS
ANDREWS

This introductory statistics course is designed not just for students majoring or minoring in math, but for any student who would benefit from a more substantial introduction to the field. In fact, about half of the students who have taken this class are not math majors. Students must learn general principles and techniques for summarizing and organizing data effectively, for designing observational studies and experiments, and for drawing specific inferences from such studies. Data analysis software is used daily. In addition to regular homework and periodic tests and quizzes, students are expected to collaborate on data analysis projects.

Prerequisite: Math Placement Level 25 (Note: A student may not receive credit for more than one of the following: MATH 127, MATH 227, PSYC 107, or MGT 210). Mathematical-reasoning intensive.

MATH 320 NUMERICAL ANALYSIS
4 SEM HRS
DAVENPORT

An introduction to the numerical solution of mathematical problems. Primary emphasis is upon the development of use of computational algorithms to obtain an accurate numerical solution as well as methods for establishing error estimates and bounds for this solution. These algorithms will primarily be implemented on the computer using the Mathematica® system. Some algorithms may also be implemented in C/C++ or FORTRAN. Some work will also be done by using a scientific graphing calculator such as the TI-83 or TI-86. This course should also be of special interest to students in the physical sciences.

Grades will be based on assignments and exams. Prerequisites: MATH 202, MATH 205, COMP 150, and familiarity with the scientific graphing calculator. This course is cross-listed as MATH 320. Students may enroll in either COMP 320 or MATH 320, but not both. Mathematical-reasoning intensive.

MATH 327 STATISTICAL MODELING
4 SEM HRS
ANDREWS

In this second course in statistics, regression analysis is the main vehicle for illustrating the principles of statistical modeling in real-world contexts. After a brief review of techniques and principles of Exploratory Data Analysis, students learn strategies for selecting and constructing models, criteria for assessing and comparing models, and tools for making formal inferences using these models. Class sessions include discussion of conceptual issues with practice in data analysis, and they put strong emphasis on interpreting and communicating the results of analyses. Students are required to collaborate on projects in which they design studies, collect and analyze data, and present their findings orally and in writing. Prerequisite: MATH 227 (or permission of instructor). Mathematical-reasoning intensive.

MATH 360 LINEAR ALGEBRA
4 SEM HRS
HIGGINS

Introduction to abstract vector spaces. Topics include Euclidean spaces, function spaces, linear systems, linear independence and basis, linear transformations and their matrices. Students are required to have a TI-83, TI-83 Plus, or TI-86 graphing calculator for use in class, for homework, and on tests. A TI-89 or TI-92 is also acceptable.

The final grade in the course is based on written assignments, quizzes, tests, and a comprehensive final exam. Prerequisites: MATH 205 and MATH 210. WRITING INTENSIVE. Mathematical-reasoning intensive.

MATH 370 REAL ANALYSIS
4 SEM HRS
HIGGINS

Through a rigorous approach to the usual topics of one-dimensional calculus - limits, continuity, differentiation, integration, and infinite series - this course offers a deeper understanding of the ideas encountered in calculus. The course has two important goals for its students: the development of an accurate intuitive feeling for analysis and of skill at proving theorems in this area.

The final grade in this course is based upon written assignments, tests, and a comprehensive final exam.

This course is intended only for junior and senior mathematics majors or minors. Others will be enrolled only with the permission of the instructor. WRITING INTENSIVE. Prerequisite: MATH 210. Mathematical-reasoning intensive.

MATH 460 SENIOR SEMINAR
2 SEM HRS
SHELBURNE

This is a capstone course for mathematics majors. Its purpose is to let participants think about and reflect on what mathematics is and to tie together their years of studying mathematics at Wittenberg. The structure of the course will be taken from the book Journey Through Genius by W. Dunham which covers the story of mathematics from the 5th century B.C.E. up to the 20th century C.E. by looking at some of the famous problems, theorems, and “colorful” mathematical characters who worked on them. The course is a seminar where participants are expected to research areas of interest in mathematics and present their findings to the rest of the seminar. The grade will be based on class discussions and presentations. Mathematical-reasoning intensive.