Trent University, Winter 2015

Mathematics 3790H

*Analysis I: Real Analysis*

MATH 3790H is an introductory course about analysis, with an emphasis on the concepts underpinning the convergence of series and the foundations of calculus.

**Prerequisite:** Mathematics 1100 or 1101Y, with at least 60%.

**Pre- or co-requisite:** Mathematics 2200H, with at least 60%.

- MATH 3790H Course Outline
- Readings and Schedule
- Assignment # 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
- Quizzes
- Final Examination
- Gauss's Test

From the online Resources for A Radical Approach to Real Analysis (2nd edition) by David Bressoud.

- Assignment # 1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11

and Solutions to Assignment # 1 - Quizzes and Quiz Solutions
- Take-Home Final Examination
- Gauss's Test

From the online Resources for A Radical Approach to Real Analysis (2nd edition) by David Bressoud.

- Assignment # 1,
2,
3,
4,
5,
6,
7,
8,
9,
10

and Solutions to Assignment # 1, 2, 3, 4, 5, 6, 7 - Quizzes and Quiz Solutions
- Take-Home Final Examination
- Gauss's Test

From the online Resources for A Radical Approach to Real Analysis (2nd edition) by David Bressoud.

- Assignment # 1,
2,
3,
4,
5,
6

Solutions to Assignment # 1, 2, 3, 4, 5 - Quizzes and Solutions to the Quizzes
- Take-Home Final Examination
- Gauss's Test

From the online Resources for A Radical Approach to Real Analysis (2nd edition) by David Bressoud.

- Assignment # 1,
2,
3,
4,
5,
6

Solutions to Assignment # 1, 2, 3, 4, 5, 6 - Quizzes and Solutions to the Quizzes
- Take-Home Final Exam
- Archimedes' summation of a series

An excerpt from his Quadrature of the Parabola, taken from The Works of Archimedes, edited by T.L. Heath, available at the Internet Archive. - Gauss's Test

From the online Resources for A Radical Approach to Real Analysis (2nd edition) by David Bressoud.

- Assignment # 1,
2,
3,
4,
5,
6

Solutions to Assignment # 1, 2, 3, 4, 5, 6 - Quizzes and Quiz Solutions
- Take-Home Final Exam

There is fair bit of material available online about real analysis and related areas; a brief selection follows:

- Analysis of Functions of a Single Variable by Lawrence W. Baggett.
- A ProblemText in Advanced Calculus by John M. Erdman.
- A first Analysis course by John O'Connor.
- Linear Partial Differential Equations and Fourier Theory by Marcus Pivato.
- Real Analysis (Second Edition), by Brian S. Thomson, Judith B. Bruckner, and Andrew M. Bruckner.
- Interactive Real Analysis by Bert G. Wachsmuth.
- Analysis WebNotes by John Lindsay Orr.
- Mathematical Analysis, Volume I, by Elias Zakon.

A lot of useful background can be found in http://www.trillia.com/zakon1.html by Elias Zakon.

- Real analysis at The Math Forum
- Resources for A Radical Approach to Real Analysis (2nd edition) [a text formerly used in this course], by David E. Bressoud.
- Real analysis at Wikipedia
- Analysis at Wolfram MathWorld

Department of Mathematics Trent University

Maintained by Stefan Bilaniuk. Last updated 2015.03.27.