MthSc 453, Summer I 2012

MthSc 453, Summer I 2012

"You see this little hole? This moth's just about to emerge. It's in there right now, struggling. It's digging it's way through the thick hide of the cocoon. Now, I could help it - take my knife, gently widen the opening, and the moth would be free - but it would be too weak to survive. Struggle is nature's way of strengthening it."
--Locke (Lost, 2004)


Class Syllabus

Text: Princples of Mathematical Analysis, by Walter Rudin. This book, affectionately called "Baby Rudin" was published in 1976 and to this day remains the gold standard of introductory real analysis texts. For an idea of why it is the best, read this friendly review.

Francis Su of Harvey Mudd College taught Real Analysis in 2010 (using Rudin's book) and the lectures were videotaped and put on YouTube. Professor Su is one of the finest teachers in the country, and was the first recipient of the Henry L. Alder Award for Distinguished Teaching, a national award given out by the Mathematical Association of America. These lectures are not a substitute for attending class, but are a great supplement. Also check out Rudinium.

• Good mathematical writing is difficult. It takes hard work and practice to acquire this skill, and developing it is of the primary goals of this class. Francis Su has written a very nice 4-page essay on the topic.

• The late Evelyn Silvia taught real analysis out of Rudin at UC Davis. She wrote a set of companion notes to go along with Rudin's book.


Homework 1: pdf | tex. Due Friday, May 18th at 4pm.
Homework 2: pdf | tex. Due Tuesday, May 22nd at 4pm.
Homework 3: pdf | tex. Due Friday, May 25th at 4pm.
Homework 4: pdf | tex. Due Tuesday, May 29th at 4pm.
Homework 5: pdf | tex. Due Friday, June 1st at 4pm.
Homework 6: pdf | tex. Due Tuesday, June 5th at 4pm.
Homework 7: pdf | tex. Due Friday, June 8th at 4pm.
Homework 8: pdf | tex. Due Tuesday, June 12th at 4pm.
Homework 9: pdf | tex. Due Friday, June 15th at 4pm.
Homework 10: pdf | tex. Due Tuesday, June 19th at 4pm.

Midterm 1 Solutions
Midterm 2 Solutions

Lecture notes

Lecture 1: Construction the rationals
Lecture 2: Properties of Q
Lecture 3-4: Constructing the reals
Lecture 5: Complex numbers
Lecture 6: Principle of induction
Lecture 7-8: Countable and uncountable sets
Lecture 8-9: Metric spaces
Lecture 10: Open and closed sets
Lecture 11-12: Compactness
Lecture 13: The Heine-Borel theorem
Lecture 14: The Cantor set and connectness
Lecture 15: Convergent sequences
Lecture 16: Subsequences and Cauchy sequences
Lecture 17: Completeness
Lecture 18: Series
Lecture 19: Convergence of series
Lecture 20-21: Limits and continuity
Lecture 22: Uniform continuity
Lecture 23: Discontinuous functions
Lecture 24-25: Differentiation