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Course Criteria
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3.00 Credits
This course offers a careful treatment of the definitions and major theorems regarding limits, continuity, differentiability, integrability, sequences, and series for functions of a single variable. Prerequisites: MATH 135 and MATH 204. ( Offered annually)
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3.00 Credits
Foundations of Analysis II
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3.00 Credits
This is an introductory course in probability with an emphasis on the development of the student's ability to solve problems and build models. Topics include discrete and continuous probability, random variables, density functions, distributions, the Law of Large Numbers, and the Central Limit Theorem. Prerequisite: MATH 232 or permission of instructor. (Offered alternate years)
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3.00 Credits
This is a course in the basic mathematical theory of statistics. It includes the theory of estimation, hypothesis testing, and linear models, and, if time permits, a brief introduction to one or more further topics in statistics ( e.g., nonparametric statistics, decision theory, experimental design). In conjunction with an investigation of the mathematical theory, attention is paid to the intuitive understanding of the use and limitations of statistical procedures in applied problems. Students are encouraged to investigate a topic of their own choosing in statistics. Prerequisite: MATH 350. ( Offered alternate years)
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3.00 Credits
Drawing on linear algebra and differential equations, this course investigates a variety of mathematical models from the biological and social sciences. In the course of studying these models, such mathematical topics as difference equations, eigenvalues, dynamic systems, and stability are developed. This course emphasizes the involvement of students through the construction and investigation of models on their own. Prerequisites: MATH 204 and MATH 237 or permission of the instructor. ( Offered every third year)
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3.00 Credits
An introduction to the axiomatic method as illustrated by neutral, Euclidean, and non-Euclidean geometries. Careful attention is given to proofs and definitions. The historical aspects of the rise of non-Euclidean geometry are explored. This course is highly recommended for students interested in secondary school teaching. Prerequisite: MATH 331 or MATH 375, or permission of the instructor. ( Offered every third year)
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3.00 Credits
Each time this course is offered, it covers a topic in mathematics that is not usually offered as a regular course. This course may be repeated for grade or credit. Recent topics include combinatorics, graph theory, and wavelets. Prerequisite: MATH 135 and MATH 204 or permission of instructor. ( Offered alternate years)
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3.00 Credits
This course studies abstract algebraic systems such as groups, examples of which are abundant throughout mathematics. It attempts to understand the process of mathematical abstraction, the formulation of algebraic axiom systems, and the development of an abstract theory from these axiom systems. An important objective of the course is mastery of the reasoning characteristic of abstract mathematics. Prerequisites: MATH 135 and MATH 204 or permission of the instructor. ( Offered annually)
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3.00 Credits
Abstract Algebra II
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3.00 Credits
First order logic is developed as a basis for understanding the nature of mathematical proofs and constructions and to gain skills in dealing with formal languages. Topics covered include propositional and sentential logic, logical proofs, and models of theories. Examples are drawn mainly from mathematics, but the ability to deal with abstract concepts and their formalizations is beneficial. Prerequisite: MATH 204, PHIL 240, or permission of the instructor. ( Offered every third year)
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