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# Math 480 - Introduction to Proofs

Credits:

Course Description: This course is intended to cover those aspects of mathematics that form a foundation for the study of advanced mathematics. In particular, it will cover such basic concepts as set theory, propositional and predicate logic, relations, functions and cardinality. In studying these concepts, the emphasis will be not only on the subject matter, which forms the core of knowledge needed to pursue more advanced mathematical courses, such as abstract algebra and real analysis, but also on how one reads and writes mathematical proofs. What constitutes a proof and various means of proving statements will be examined in detail during the course. As time permits we will then apply these topics and methods to specific areas, such as the study of calculus (the epsilon-delta definition of limit, continuity, differentiation, sequence and series), group theory (binary operations, fundamental properties of groups, subgroups, isomorphic groups) and linear algebra.

Pre-Requisites: MATH 260 - Linear Algebra

Note: this special topics course will serve as a 300-level mathematics elective for mathematics majors or minors. In the future, if the course, or a modified version of it, is approved by the department and university governance, then it may become a required course for the mathematics major and be a prerequisite for courses like MATH 360 - Abstract Algebra Iand MATH 450 - Real Analysis. It should not be taken after MA 360 or MA 450.

Frequency:

Current Textbook: Mathematical Proofs: A Transition to Advanced Mathematics, Second Edition, by Chartrand, Polimeni and Zhang, published by Pearson Addison Wesley in 2008. Check with your instructor to make sure this is the textbook used for your section.

Fall 2011 Schedule:
Section Meeting Time Topic Instructor
1 MWF 11:00am-11:50am Introduction to Proofs Dennis Wortman

Topics
• 0. Communicating mathematics (how to read and write mathematics)
• 1. Sets
• 2. Logic
• 3. Direct proof and proof by contradiction
• 4. More on direct proof and proof by contradiction
• 5. Existence and proof by contradiction
• 6. Mathematical induction
• 7. Prove or disprove
• 8. Equivalence relations
• 9. Functions
• 10. Cardinalities of sets
• 11. Proofs in calculus
• 12. Proofs in group theory

The order of presentation of the contents of this syllabus, exams, and grading policies are entirely at the discretion of the individual instructor.

 Questions and suggestions regarding this page should be addressed to math-web@math.umb.edu Department of Mathematics University of Massachusetts Boston Phone: 617-287-6460;   Fax: 617-287-6433 Information: math-info@math.umb.edu