Harvard University, fas   
Fall 2003   

Mathematics 55a


  • Instructor.

    Yum-Tong Siu (siu@math.harvard.edu),
    William Elwood Byerly Professor of Mathematics,
    Science Center 511, Tel:495-3790.

  • Office Hours.

    MWF 1 p.m. - 2 p.m.

  • Textbooks.

    • Walter Rudin,
      Principles of Mathematical Analysis.
      McGraw-Hill, 3rd Edition
    • Sheldon Axler,
      Linear Algebra Done Right.
      Springer, 2nd Edition
  • Course Assistant. 

    Ian T. Le (ile@fas.harvard.edu),

    Telephone: 3-3093

    Office Hours: Thursday, 8 p.m. - 10 p.m., Lowell Dining Hall

  • Major Topics.

    The course will basically cover Rudin, Chapters I-IV and Axler, Chapters I-X, including the following topics:

    • The Real and Complex Number Systems

    • Basic Point-Set Topology

    • Numerical Sequences and Series

    • Continuity

    • Vector Spaces and Linear Maps

    • Eigenvalues and Eigenvectors

    • Inner-Product 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 first-year students are tempted to skip Math 25/Math 55 altogether and go right into the upper-level 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 in-class 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 take-home exam. For the final take-home exam you will be on your honor to work completely on your own.

  • Grades. Two-third of the course grade will be based on the homework problem sets and the quizzes. The final take-home exam will account for almost all of the remaining one-third 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.


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last modified: 09/12/2003

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