James K. Brooks, Professor , Department of Mathematics
e-mail:  jkbrooks@ufl.edu

Course title: Elementary differential equations, SPRING 2012 , MAP 2302, LIT201, section 022H

Office hours: MW 6, LIT306 or by appointment

Please see below the course offered in FALL 2011.  Everything will be the same except test dates.

Test Dates are (in class period 5) :  Feb 1, Feb 29, April 4, April23,April 25.

Course title: Analysis, FALL 2011, MAA6616, section 3053
Instructor: J. Brooks, Little 306, jkbrooks@ufl.edu
Office hours:  MF 6  or by appointment
Text:  Measure Theory by P.R. Halmos

This first semester in Analysis is designed to lay the foundations of modern analysis and
applications.  The first eight chapters of Halmos' book will be covered in addition to
various other topics which will be the foundation for the functional analysis in the second semester.

Most of the problems listed in the book will be assigned.  These and other complementary
problems constitute a very important part of the course.  Grades are based on numerous
quizzes, tests, a comprehensive final exam and class participation.  The essential background
for the course is mastery of the content of the introductory analysis sequence  MAA 5228-9.

The second semester will include, time permitting, topics in stochastic processes and
martingale theory which will further illuminate the first semester material.

Course title:  Elementary Differential Equations,  FALL 2011,  MAP 2302, section 5607
Instructor:             J. Brooks, Little 306, jkbrooks@ufl.edu
Office hours:  MF 6  or by appointment
Text: Differential equations and boundary problems, 6th edition , by Nagle,Saff, Snider

This course is designed to introduce some methods to solve certain types of differential equations.
Prerequisites include swift calculations of derivatives and integrals and algebraic manipulation.
It is important to keep up to date on the various methods presented.  Problem assignments will
be posted on the board in calss.  Some of the problems and examples in the book (in modified form)
may appear on the tests.  There will be 3 tests given during the term in class:  Sept 21, Oct 19,
Nov 16,  each test is worth 20% of the grade.  A comprehensive final will be worth 40%.
A grade of  0  will be given for a missed test.  In the event of a medical emergency an
accomodation may be considered with a complete documented doctor's letter. If it  is ascertained
that 5 classes have been missed, an E grade will be given.

If you should miss a class be sure to obtain the assignment and notes from a fellow student
since some material may not be in the text.  No aids or calculators are to be used for tests.
 Any student  who plans to participate in the Disability Resource Center must contact me
after their first class meeting.

Course material will include Ch 1, Ch2 topics from Ch 3,5,    Ch 4(4.2-4.7), Ch 8,
depending on time constraints.

The most severe grading scale is the standard one:  100-90 A, 89-85 B+, etc.






2007-2008  Functional Analysis  MAA 7526-7
Fall   MWF 7  Little 217
Prerequisites:  MAA6617 or permission of the instructor  No text required

This course is designed to introduce the student to Banach spaces, Hilbert
spaces and locally convex spaces.  The main theorems concerning these
spaces will be presented, along with various applications.  Some of the topics
include:  structure of compact operators, spectral theory, the spectral
representation of normal operators, perturbation theory, theory of distributions,
Fourier transforms, inductive limits, Sobolev space theory, Fredholm theory.

The course will be conducted as a seminar and additional topics reflecting
student needs may be added, e.g. unbounded operators, etc.



Course: History of Mathematics MHF 3404  section 4822  MTWRF 4  LIT 201
              Summer B
Instructor: J.K. Brooks  LIT 364 Office hours MWF 1:45-2:30

Text: The New Golden Age by Keith Devlin, New and revised edition
          paperback,  Campus Bookstore

This course will examine some of the significant developments that have taken place
in "recent" times and discuss the history behind the concepts.  Topics will be taken
(time permitting) from the following areas: Number theory, Set Theory, Group Theory,
Probability Theory, Structure of the real line, Einstein's contributions.

Some material is based on the textbook, some will be based on my notes.  Tests will be
given at the end of weeks 2,4,6.  A standard grading scale will be used. Five or
more ascertained absences will result in a failing grade.  A missed test counts as a
zero grade (unless very compete medicat documentation is provided).










MAT 6932  Introduction to Hilbert Space  Summer 2007  Little 127 Period 6

Hilbert space and the theory of operators on Hilbert space is one of the most
important topics in mathematics and this theory is used in all branches of science.
In this course we shall cover the geometry of Hilbert space and begin a study
of the algebra of operators on Hilbert space, which will lead to the spectral
theorem of von Neumann for normal operators.

No text is required.  The course will be conducted in the format of a seminar
and no tests will be given.  Good attendance and careful note-taking are
required.

MAA 5228-9 or the equivalent is the prerequisite.