
Instructor.
YumTong Siu (siu@math.harvard.edu),
William Elwood Byerly Professor of Mathematics,
Science Center 511, Tel:4953790.

Office
Hours.
MWF 1 p.m.  2 p.m.

Textbooks.

Walter Rudin,
Principles of Mathematical Analysis.
McGrawHill, 3rd Edition
 Sheldon Axler,
Linear Algebra Done Right.
Springer, 2nd Edition

Course
Assistant.
Ian T. Le (ile@fas.harvard.edu),
Telephone: 33093
Office Hours: Thursday, 8 p.m.  10 p.m., Lowell Dining Hall

Major
Topics.
The course will basically
cover Rudin, Chapters IIV and Axler, Chapters IX, including the
following topics:

The Real and Complex Number Systems

Basic PointSet Topology

Numerical Sequences and Series

Continuity

Vector Spaces and Linear Maps

Eigenvalues and Eigenvectors

InnerProduct Spaces and their Operators

Operators on Real and Complex Vector Spaces

Trace and Determinants
Additional topics will be included as time permits.
Most of the topics covered in Math 55a will be used in Math 55b to develop a rigorous
treatment of differential and integral calculus in one and several variables, and also to sample other topics such as differential equations and Fourier analysis.

Prerequisites and Comparison with Math 25.
Math 55 is intended for students with significant experience with and enthusiasm for abstract
mathematics. Its syllabus is similar to that of Math 25. Math 55 differs from Math 25 not so much in
the choice of topics as in the level of exposition.
The Mathematics Department offers these courses at separate hours so that you can "shop" both, which you are strongly encouraged. You may switch between Math 55 and Math 25 without penalty for the first three weeks of the semester.
N.B. Each year several firstyear students are tempted to skip Math 25/Math 55 altogether and go right into the upperlevel undergraduate or graduate courses. From our past experience, in nearly all cases it is best to resist such a temptation.

Homework.
Weekly problem sets will be given on Friday and due in class the
following Friday. Late homework will not be accepted.
You are encouraged to discuss the course with other students, your Course Assistant, and me.
It is much easier to learn mathematics if you have other people who will help you test your
understanding and overcome problems. It is fine to discuss homework problems with other students,
but you should always write your homework solutions out yourself in your own words and understand them.

Quizzes.
There will be two inclass quizzes that will test your recollection of basic concepts. Each quizz
will count for the equivalent of one homework problem set.

Final.
The Final Exam will be a takehome exam. For the final takehome exam you will
be on your honor to work completely on your own.

Grades.
Twothird of the course grade will be based on the homework problem sets and the quizzes. The
final takehome exam will account for almost all of the remaining onethird of the course grade,
with class participation used mostly to decide on borderline cases.
The course is not
graded on a curve. The grade is based only on the performance of each individual student and not on the relative standing of the student in the whole class. The assignment of grades is not constrained by any rule of a fixed percentage for any particular grade.