MATH 112 The Language of Mathematics Prerequisite: Math Placement Level 22 or higher
(4 credits)
Barhorst, Garry
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 TeachersPrerequisite: 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, communicating mathematically, and making connections within mathematics and between mathematics and other areas. Open only to students intending to major in education. Every year. Mathematical-reasoning intensive.
MATH 119 Geometry with Computer Applications for Elementary and Middle School TeachersPrerequisite: MATH 118
Study of basic concepts of plane and solid geometry, including topics from Euclidean, transformational, and projective geometry. Includes computer programming experiences using Geometer=s Sketchpad. Every year. Mathematical-reasoning intensive.
MATH 120 Elementary FunctionsPrerequisite: 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 StatisticsPrerequisites: Math Placement Level 23 or higher
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.
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 CalculusPrerequisite: MATH 120 or Math Placement Level 25
This one semester calculus course is an introduction to the techniques and applications of differential and integral calculus. The applications come primarily from the economics and bio-sciences and do not involve any trigonometric models. 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.
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.
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 or minoring in mathematics, computer science, physics, or chemistry. MATH 201 and MATH 202 can also count as Asupporting 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: AEssentials of Calculus@. Talk with your advisor or with any math professor for advice on which calculus course is most appropriate for you.
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. Depending on the instructor, 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 IIPrerequisite: 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, elementary differential equations, approximations of definite integrals, improper integrals, applications of integrals, power series, Taylor=s 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 homework, quizzes, tests, and a comprehensive final exam. Mathematical-reasoning intensive.
MATH 210 Fundamentals of AnalysisPrerequisite: MATH 202
Functions, set theory, sequences, the topology of the real line, and methods of mathematical proof. Particular emphasis is given to careful, accurate definition and proof of mathematical concepts. Grades may be based on several tests, quizzes, homework assignments, and a final examination. WRITING INTENSIVE. Mathematical-reasoning intensive.
MATH 212 Multivariable CalculusPrerequisite: MATH 202
This course completes the basic calculus sequence. It covers the calculus of functions of several variables and associated analytic geometry. 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. The final grade in the course is based on quizzes, tests, and a comprehensive final exam. Mathematical-reasoning intensive.
MATH 260 Computational Models and MethodsPrerequisites: (1) MATH 131 or MATH 201 (2) COMP 150 or equivalent experience as determined by the instructor
Computational science is the field of study that integrates science, computer science, and applied mathematics. This course is an introduction to the principles and approaches of computational science. This includes the understanding, development, and use of mathematical models as well as their effective computer implementation using computer languages such as Mathematica®. This course is specifically designed to be accessible to a wide range of students, especially those with an interest in applications of biology, chemistry, geology, physics, or economics.
A spectrum of problems taken from these areas will be addressed. Topics include: Using Mathematica®, The Scientific Process, The Experimental Method, Types of Science Models (for Evaluation, Simulation, and Optimization), Sources of Errors, Dimensional Analysis, Model Sensitivity, Solving Equations, Computer Arithmetic vs. Exact Arithmetic, Limits of Computation, Data Fitting, Visualization Methods, and Ethical Issues. Applications of computational science in our everyday lives will be investigated. A weekly two hour and ten minute computer laboratory is required. The student will be expected to be familiar with the use of a scientific graphing calculator. This course is cross-listed as MATH 260. Students may enroll in either COMP 260 or MATH 260, but not both. Mathematical-reasoning intensive.
MATH 271 Discrete Mathematical StructuresPrerequisite: MATH 131 or MATH 201
Discrete Mathematical Structures covers a number of mathematical topics which are central to both mathematics and computer science, topics centering on the mathematics of discrete sets, that is, sets which are finite or at most countably infinite. Starting on the foundation of logic, set theory and basic proof techniques the course will cover relations and functions, counting arguments, discrete probability, number theory and graph theory. The course is required for the major and minor in computer science and can be used as an elective for the mathematics major. The course grade will be determined by quizzes, graded homework assignments, in-class tests and a comprehensive final.
MATH 337 Statistical DesignPrerequisite: MATH 227
Whereas the introductory statistics sequence focuses primarily on exploratory and formal analysis of data that have already been observed, this course focuses primarily on how to design the comparative observational and experimental studies in which data is collected for formal analysis. Students will learn: 1) to choose sound and suitable design structures, 2) to recognize the structure of any balanced design built from crossing and nesting, 3) to assess how well standard analysis assumptions fit the given data and to choose a suitable remedy or alternative when appropriate, 4) to decompose any balanced dataset into components corresponding to the factors of a design, 5) to construct appropriate interval estimates and significance tests from such data, and 6) to interpret patterns and formal inferences in relation to the relevant applied context. Students are required to collaborate on projects in which they design studies, collect and analyze data, and present their findings orally and in writing. Students who have taken a different introductory statistics course may be admitted with permission of instructor. Mathematical-reasoning intensive.
MATH 365 Abstract AlgebraPrerequisite: MATH 205 and MATH 210
This course will focus on abstract algebraic structures such as groups, rings, and fields with particular attention to groups. There will be an emphasis on presenting arguments with a full explanation of the reasoning. Grades will be based on written homework, work done in class, and exams. WRITING INTENSIVE. Mathematical-reasoning intensive.
MATH 380 Computational Algebraic GeometryPrerequisite: MATH 205
Algebraic geometry is the study of systems of polynomial equations in one or more variables. The solution to such a system is a geometric object called a variety and much of algebraic geometry is concerned with how algebraic properties of the system are related to geometric properties of the variety. Results in this field tend to be quite abstract and complexity increases rapidly, making examples hard to compute. This changed in the mid 1960’s with the discovery of a generalized division algorithm called Buchberger’s algorithm. With this new computational tool, it became possible to manipulate systems of polynomials efficiently. As a result, algebraic geometry has become accessible to a wider audience of both students and researchers.
This course will concentrate on the algorithmic and computational aspects of algebraic geometry. Topics covered will include, but not be limited to Hilbert Basis Theorem, the Nullstellensatz, resultants, and Buchberger’s algorithm. The final course grade will be based on homework, tests, class participation, and a computer project. Mathematical-reasoning intensive.
