Written Exam Workshop

Fall 2009

Fall 2009

Will Perkins

perkins@cims.nyu.edu

office 1111

office hours: Mondays, 7 - 8 pm (note the change)

schedule

practical information

links

references

schedule

Week 1 (9/17) - Calculus

Topics: Limits and Series; tests of convergence

Worksheet

Week 2 (9/24) - Calculus

(there will be a subsitute instructor this week)

Topics: Multivariable calc; Green's / Stokes' / Divergence Theorem. Polar / spherical coordinates. Tangents, normals, Implicit Function Theorem. Optimization Problems.

Worksheet

Homework (for today): S07 #2, S06 #3, S05 #4, J05#4, S03 #5, S03 #4

Week 3 (10/1) - Linear Algebra

Topics: Solving Linear Equations; Det, Trace, Characteristic Poly; Diagonalizing; Block Matrices; Projections

Worksheet

Homework: S98 #5, J00 #3, J02 #1, S02 #2, S03 # 1, J07 #1

Week 4 (10/8) - Advanced Calculus

Topics: Improper Integrals, Limits of Integrals, Infinite Products.

90-second student presentations on special types of matrices

Worksheet

Homework: S03 #1, J07 #2, J04 #2, J99 #2, S98 #4, S98 #3, S96 #1

Week 5 (10/15) - Complex

Topics: Conformal Maps; Liouville's Theorem; Schwartz's Lemma; Rouche's Theorem

Worksheet

Homework: S07 #3, S07 #4, S07 #5, J07 #4, J06 #5, S05 #5

Week 6 (10/22) - Linear Algebra

Topics: Decompositions; Graham Schmidt; Rayleigh Quotient

Worksheet

Homework: J07 #4, J07 #5, S04 #3, J04 #3, J01 #4, J98 #5

Week 7 (10/29) - Advanced Calculus

Topics: Optimization, Functional Equations, Fourier Stuff,

Worksheet

Homework:

Week 8 (11/5) - Complex

Topics: Analytic continuation, branch cuts, Schwartz-Christoffel mapping,

Worksheet

Homework: J98 #4, S98 #5, S99 #4, J01 #1, J02 #5, J02 #1

Week 9 (11/12) - Advanced Calculus

Topics: More Multivariable Calculus

Worksheet

Homework: No specific problems assigned - we'll be going over the basic methods. But look through the past problems and come in with any that you have questions about.

Week 10 (11/19) - Linear Algebra

Topics: Jordan form, least squares, + assorted problems

Worksheet

Homework: J 98 #2, J 96 #4, S 96 #3, J 97 #2, J 99 #5, J 02 #2, J 06 #5

Thanksgiving (11/26)

Week 11 (12/3) - Complex

Topics: Harmonic functions, Poisson Integral Formula, Infinite Products,

Worksheet

Homework: S95 #4, S99 #5, J03 #4, J05 #5, S05 #4, J07 #2

Week 12 (12/10) - Review

Topics: Review of all 3 subjects + practice problems of crucial types.

REVIEW SHEET

Homework: Prepare and bring to class an outline of each subject, dividing it into different categories and types of problems. For the types of problems you still need to review, add references and practice problems.

practical information

- The most important thing for you to do is pick up a copy of the
past written exams from Tamar's office!

- Each week I'll assign 6 or so past written exam problems to do
for the next week. I strongly enocurage you to do/try them.
We'll go over the key points of the solutions in class , but if you'd
like to see the details flushed out, just stop by my office.

- Please print out the worksheet and any handouts before each class. I'll bring a few copies in case you forget, but not enough for the whole class.
- Give me lots of feedback about what you want covered, how fast we're going, etc. The mix of the topics covered should depend on what you guys want to learn.
- The best advice I can give you? Do lots and lots of
problems!

links

- Evan Chou's Writtens Wiki
- Andrew Suk's Writtens Solutions
- Miranda Holmes' Fall 07 Written
Workshop page

references

General

- Berkeley
Problems in Mathematics,
De Souza & Silva. A ton of collected problems from Berkeley's
version of the written exams, with solutions. Not quite the same
topics as we have, but a good place to see a lot of useful
techniques.

- Problems
and Theorems in Analysis I: Series, Integral Calculus, Theory of
Functions (Classics in Mathematics), Polya & Szego. Sort of
old-timey and more
difficult than the problems you'll see, this does contain some problems
that have appeared before and is written by the master problem solver.

- Advanced
Calculus,
Buck. Spells out some of the more difficult techniques of taking
limits of integrals.

- Differential and Integral Calculus (2 Volume Set), Courant. Besides writing this excellent book, the author also founded this school.
- Div,
Grad, Curl, and All That: An Informal Text on Vector Calculus, Fourth
Edition,
Schey. Useful if, like me, you are completely lost when calculus
and vectors meet.

Linear Algebra

- Introduction
to Linear Algebra, Fourth Edition,
Strang. Thorough and readable of the basics.

- Linear
Algebra and Its Applications (Pure and Applied Mathematics: A Wiley
Series of Texts, Monographs and Tracts),
Lax. Good on the abstract stuff. You can also get your copy
autographed here if you're lucky.

- Numerical
Linear Algebra,
Trefethen & Bau. Very good on some of the stuff you won't see
in the introductory class: the different decompositions, like SVD,
Choelesky, etc. Very useful!

Complex

- Complex Variables and Applications, Churchill & Brown. The complex analogue of Strang.
- Functions
of One Complex Variable (Graduate Texts in Mathematics - Vol 11) (v. 1),
Conway. My personal favorite.