NOTE. All homework and exam solutions have been temporarily removed. They will be
returned to this website once I am done teaching the Math 395/396 sequence in 2010-2011.

My office is 4859 East Hall, and my office hours are 3-6pm on Wednesdays and by appointment.

The twitter link for the course is HERE

Syllabus in PDF

Take-home final exam in PDF
Final exam solutions in PDF

Take-home midterm in PDF
Midterm solutions in PDF



No solutions will be posted for Homework 3
Homework 4 (due Friday, October 9, at the beginning of class) in PDF
Solutions to Homework 4 in PDF
Homework 5 (due Friday, October 16, at the beginning of class) in PDF
Solutions to Homework 5 in PDF
Homework 6 (NOT DUE) in PDF
No solutions will be posted for Homework 6
Homework 7 (due Friday, November 6, at the beginning of class) in PDF
Solutions to Homework 7 in PDF
Homework 8 (due Friday, November 13, at the beginning of class) in PDF
Solutions to Homework 8 in PDF
Homework 9 (due Friday, November 20, at the beginning of class) in PDF
Solutions to Homework 9
Homework 10 (due Friday, December 4, at the beginning of class) in PDF
Solutions to Homework 10 in PDF
Homework 11 (due Friday, December 11, at the beginning of class) in PDF
Solutions to Homework 11

1. Bilinear forms; symplectic and quadratic forms (week of September 7)
   
   • Summary of lecture 1 (09/08/2009) in PDF
   • Summary of lecture 2 (09/09/2009) in PDF
   • Summary of lecture 3 (09/11/2009) in PDF
      
2. Jordan normal form of linear operators (week of September 14)
   
   • Summary of lecture 4 (09/14/2009) in PDF
   • Summary of lecture 5 (09/15/2009) in PDF
   • Summary of lecture 6 (09/16/2009) in PDF
   • Lecture 7 (09/18/2009) was devoted to a description of an algorithm
     for finding the Jordan normal form of a given linear operator. At this
     point I don't have a typed up summary (I might post one later).
      
3. First and second derivatives of functions of several variables (week of September 21)
   
   • Summary of lecture 8 (09/21/2009) in PDF
   • Summary of lecture 9 (09/22/2009) in PDF
   • Lecture 10 (09/23/2009) was devoted to a proof of the theorem that
     if all partial derivatives of a function exist in an open neighborhood of
     a point x and are continuous at x, then the function is differentiable at x.
     There will be no summary posted (the proof can be found in Munkres).
   • Summary of lecture 11 (09/25/2009) in PDF
      
     
4. Introduction to measure theory and integration (week of September 28)
   
   • Summary of lecture 12 (09/28/2009) in PDF
   • Lecture 13 (09/29/2009) was mainly devoted to discussing the
     future plans for the course and the motivation behind the notion
     of the Lebesgue integral. There will be no summary posted.
   • Summary of lecture 14 (09/30/2009) in PDF
   • Summary of lecture 15 (10/02/2009) in PDF
      
5. Fundamental theorems of integration theory (week of October 5)
   
   • Summary of lecture 16 (10/05/2009) in PDF
   • Summary of lecture 17 (10/06/2009) in PDF
   • Summary of lecture 18 (10/07/2009) in PDF
   • Summary of lecture 19 (10/09/2009) in PDF
      
6. Proof of Fubini's theorem and introduction to L^p spaces (week of October 12)
   
   • Sketch of proof of Fubini's theorem in PDF
     
   • Summary of some basic results on L^p spaces in PDF
      
7. Some basic results on L^p spaces (week of October 19)
   
   • The week was devoted to Jensen's inequality and Hölder's inequality
   • There will be no notes posted for the week
      
8. Continuation of the discussion of L^p spaces; introduction to probability theory (week of October 26)
   
   • Proof of Minkowski's inequality in PDF
   • Completeness of L^p spaces in PDF
   • An invitation to probability theory in PDF
      
9. Some more probability theory and an introduction to Fourier transforms (week of November 2)
   
   • Strong laws and applications in PDF
   • Weierstrass approximation theorem in PDF
   • Introduction to Fourier transforms (Friday, November 6). No notes will be
     posted for this lecture, but most of what was covered is contained in the
     notes for the Monday, November 9 lecture (see below).
      
10. Fourier transforms: definitions and computational aspects (week of November 9)
    
    • Basic properties of Fourier transforms in PDF
    • Real and complex measures in PDF
    • Explicit calculation of Fourier transforms
       
11. Fourier transforms, continued (week of November 16)
    
    • The Residue Theorem and applications
    • A bit of complex analysis in PDF
    • Other explicit Fourier transform computations in PDF (to appear eventually)
       
12. Fourier transforms, continued (week of November 23)
    
    • Schwartz functions
    • Fourier inversion theorem
    • Plancherel's formula
    • Fourier transform for L^2 functions
    • Notes on the topics listed above in PDF
    • A brief introduction to distributions in PDF (to appear eventually)
       
13. Convolutions and related topics (week of November 30)
    
    • Intuitive meaning of convolution
    • Use of convolution for smoothing functions
    • Relation between convolutions and Fourier transforms
    • Convolution of functions with measures and distributions
    • Notes for the week in PDF
       
      
14. Numerical calculation of Fourier transforms (week of December 7)
    
    • Trapezoid rule and numerical integration
    • Fourier transform on finite abelian groups
      
    • Fast Fourier transforms
    • Poisson summation formula
    • Accurate error estimates for FFT
    • Notes for the week in PDF (to appear eventually)