# Mathematics - Fall 2014

**MATH 090 Introductory Algebra and Probability Using ALEKS****0 credits****Lewis, Obed**

**Prerequisite: Enrollment requires approval of the Director of the Math Workshop. **

A graded, non-credit course moving from elementary algebra through more complex concepts, with the objective of producing readiness for college-level work in mathematics and math-related courses. Topics include real numbers, simple operations on polynomials, solving and graphing linear equations, algebraic fractions, fractional equations, and exponential and logarithmic functions, as well as other more advanced topics which will prepare students for statistics or pre-calculus if desired. This course is taught using a web-based, artificially intelligent assessment and learning system called ALEKS which individualizes the curriculum to the students’ needs. A grade of 80% or higher in the respective ALEKS course (Math Placement Level 22, 23 or 24) constitutes a passing grade in MATH 090. This course only serves to help students raise the second digit of their math placement score.

**MATH 112 The Language of Mathematics****4 credits****Staff**

**Prerequisite: Math Placement Level 22 or higher**

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. This course is not intended to prepare students for further courses in mathematics. Mathematical-reasoning intensive.

**MATH 118 Mathematics for Elementary and Middle School Teachers****4 credits****Post**** ****Prerequisite: Math Placement Level 22 or higher**

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 and proof, communicating mathematically, and making connections within mathematics and between mathematics and other disciplines. Open only to students intending to major in education. Every year. Mathematical-reasoning intensive.

**MATH 119 Geometry with Computer Applications for Elementary & Middle School Teachers****2 credits****Post**

**Prerequisite: MATH 118**

Study of basic concepts of plane and solid geometry, including topics from Euclidean, transformational, and projective geometry with a special emphasis on the processes of mathematics: problem solving, reasoning and proof, communicating mathematically, and making connections among mathematical ideas, real-world experiences, and other disciplines. Includes computer lab experiences using Geometer’s Sketchpad. Open only to students majoring in education. Every year. Mathematical-reasoning intensive.

**MATH 120 Elementary Functions****4 credits****Ben-azzouz, Moez/ Staff**

**Prerequisite: Math Placement Level 24 or higher **

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 will be based on homework, quizzes, tests, and a comprehensive final exam. Students are required to have a TI-83, TI-84, or TI-86 graphing calculator for use in class and for homework assignments. Mathematical-reasoning intensive.

**MATH 127 Introductory Statistics****4 credits****Staff**

**Prerequisites: Math Placement Level 23 or higher**

A study of statistics as the science of using data to glean insight into real-world problems. Includes principles and 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.

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 201 Calculus I****4 credits****Staff**

**Prerequisite: MATH 120 or Math Placement Level 25**

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 in mathematics, physics, or chemistry, or minoring in mathematics. 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”. Students majoring in computer science must take either Math 131 or Math 201/202. 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-84, 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.

The final grade in the course could be based on homework, quizzes, tests, and a comprehensive final exam. Mathematical-reasoning intensive.

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

**MATH 202 Calculus II****4 credits****Staff**

**Prerequisite: MATH 201 **

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, approximations of definite integrals, improper integrals, applications of integrals, power series, Taylor series, geometric series, and convergence tests for series.

Normally, students are required to have a TI-83, TI-84, 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.

The final grade in the course will be based on quizzes, tests, and a comprehensive final exam. Mathematical-reasoning intensive.

**MATH 205 Applied Matrix Algebra****4 credits****Staff**

**Prerequisites: MATH 201**

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-84, or TI-86 calculator for use in class, for homework, and for tests. A TI-89, TI-92, or Voyage 200 is also acceptable. The final grade in the course is based on quizzes, tests, and a comprehensive final exam.

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

**MATH 215 Differential Equations****4 credits****Staff**

**Prerequisite: MATH 202**

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, homework and a comprehensive final exam. Mathematical-reasoning intensive.

**MATH 227 Data Analysis****4 credits****Andrews, Douglas**

**Prerequisite: MATH 131 or MATH 201**

This introductory statistics course is designed not only for students majoring or minoring in math, but for any student who would benefit from a more substantial introduction to the field - especially prospective teachers of mathematics or statistics, as well as students considering careers as statisticians or actuaries. Students will learn general principles and techniques for summarizing and organizing data effectively, and will explore the connections between how the data was collected and the scope of conclusions that can be drawn from the data. Also emphasized are the logic and techniques of formal statistical inference, with greater focus on the mathematical underpinnings of these basic statistical procedures than is found in other introductory statistics courses. Software for probability and data analysis is used daily.

Note: A student may not receive credit for more than one of the following: MATH 127, MATH 227, PSYC 107, or BUSN 110. Mathematical-reasoning intensive.

**MATH 228 Univariate Probability****4 credits****Andrews, Douglas**

**Prerequisite: MATH 131 or MATH 202 **

Probability is the branch of math in which we study randomness and quantify uncertainty. This course introduces some of the theory and applications of probability for a single variable. Topics include combinatorics, probability axioms, discrete and continuous random variables. This material constitutes one third of the first actuarial exam. Anyone interested in pursuing actuarial science or statistics should certainly take this course, and it would be a great elective for any math major or minor. Mathematical-reasoning intensive.

**MATH 360 Linear Algebra****4 credits****Staff**

**Prerequisites: MATH 205 and MATH 210 **

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-84, or TI-86 graphing calculator for use in class, for homework, and on tests. A TI-89, TI-92, or Voyage 200 is also acceptable.

The final grade in the course is based on written assignments, quizzes, tests, and a comprehensive final exam. Writing intensive. Mathematical-reasoning intensive.

**MATH 370 Real Analysis****4 credits****Staff**

**Prerequisite: MATH 210 **

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. Writing intensive. Mathematical-reasoning intensive.

**MATH 460 Senior Seminar****2 credits****Shelburne, Brian**

**Prerequisite: Senior math major or permission of instructor**

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, problem write-ups, in class presentations and an expository paper on some mathematical subject. Mathematical-reasoning intensive. Writing intensive.