This site is devoted to mathematics and its applications. Created and run by Peter Saveliev.

Intro to Higher Mathematics -- Spring 2016

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MTH 300 - Intro to Higher Mathematics. A transition between elementary calculus and higher mathematics with emphasis on techniques of proof. (PR: C or better in MTH 230)

  • Time and Place: 1:00 pm - 1:50 pm MTWR 509 Smith Hall
  • Instructor: Peter Saveliev (call me Peter)
  • Office: Smith Hall 713
  • Office Hours: MW 2:30-4:45 (walk-in), or by appointment
  • Office Phone: x4639
  • E-mail: saveliev@marshall.edu
  • Class Web-Page: math02.com
  • Prerequisites: a certain level of mathematical maturity acquired through experience with calculus, algebra, geometry, etc.
  • Text: How to read and do proofs by Solow
  • Outcomes: the student will become proficient at reading proofs, checking proofs, discovering proofs, and writing proofs; the student will also start to become familiar with various constructions of advanced mathematics.
  • Activities: the student will practice each outcome via the homework given in the textbook and online.
  • Evaluation: the student achievement of each outcome will be assessed via
    • homework and quizzes: 40%
    • midterm: 25%
    • final exam: 35%

See also Course policy.

1 Lectures

Student's guide to proof writing

The lectures -- exactly as they appear in class -- will be linked here and updated on a daily basis:


2 Chapters

  • 1 The truth of it all 1
  • 2 The forward-backward method 9
  • 3 On definitions and mathematical terminology 23
  • 4 Quantifiers I : the construction method 35
  • 5 Quantifiers II : the choose method 45
  • 6 Quantifiers III : specialization 59
  • 7 Quantifiers IV : nested quantifiers 69
  • 8 Nots of nots lead to knots 79
  • 9 The contradiction method 87
  • 10 The contrapositive method 99
  • 11 Uniqueness methods and induction 107
  • 12 Either/or and max/min methods 123
  • 13 Summary 135

3 Notes

Upcoming: