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

# Intro to Higher Mathematics -- Spring 2016

### From Mathematics Is A Science

**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:

- Intro to Higher Mathematics -- Spring 2016 -- midterm: Wednesday, March 9
- Intro to Higher Mathematics -- Spring 2016 -- final exam, Friday May 6, 12:45-2:45 pm, same place. (Note: If the two-hour time allowance results in a conflict in exam times, it is the student’s responsibility to notify the professor of the later course and to reschedule the later exam.)