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%.

Handouts & Work

Winter 2015

• 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.

Winter 2014

• 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.

Fall 2012

• 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.

Fall 2010

• 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.

Fall 2009

• 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.

Fall 2008

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

Other sources

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

Some notes and texts available online

• 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.

Some other real analysis references and resources online

• 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