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)
Resources
• 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
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