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Math 310

Introduction to Mathematical Reasoning

Math 310 is a course emphasizing mathematical arguments and the writing of proofs. The course gives students the opportunity to learn how to formulate mathematical arguments in an elementary mathematical setting. It serves as a complement to calculus by introducing ideas of discrete mathematics. In addition to forming a foundation for more abstract mathematics it should appeal to students preparing to be teachers or computer scientists.

The topics are:

  • the language and notation of elementary set theory,
  • elementary examples of functions and operations on functions,
  • the principle of induction,
  • counting,
  • elementary number theory,
  • elementary combinatorics,
  • recurrence relations.

    The text, Mathematical Thinking by John D'Angelo and Douglas West, introduces a list of interesting problems and maintains a focus throughout on the solution of such problems. The student learns the need for rigorous mathematical argument in obtaining valid solutions.

    The syllabus will vary a bit, depending on the instructor. The core syllabus for Math 310, using D'Angelo and West is as follows:

    • Chapter 1 (Numbers, Sets and Functions): less than 1 week
    • Chapter 2 (Language and Proofs): 1 1/2 - 2 weeks
    • Chapter 3 (Induction): 1 week
    • Chapter 4 (Bijections and Cardinality): 1 1/2 - 2 weeks
    • Chapter 6 (Divisibility): 1 week
    • Chapter 7 (Modular Arithmetic): 1 1/2 - 2 weeks

    Depending on the instructor, portions of these additional chapters would be covered, with possible supplementary material:

    • Chapter 5 (Combinatorial Reasoning)
    • Chapter 8 (Rationals)
    • Chapter 9 (Probability)
    • Chapter 10 (Two Principles of Counting)
    • Chapter 12 (Recurrence Relations)

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