Math 401/501 - Advanced Calculus I

MATH 401/501 - Avanced Calculus I
Spring 2014

This class is cross-listed as:

Homework
Review 1 Solutions Midterm 1

Textbook: Analysis I - Second Edition, by Terence Tao. Text and Readings in Mathematics 37. Hindustan Book Agency 2009 (required). Here you will find the first four chapter of Tao's book in pdf format pdf file. Terence Tao is an exceptional mathematician who has earned almost all possible awards a mathematician can get, including the 2006 Fields Medal (the equivalent of a Nobel Price in Mathematics). He also cares deeply about teaching, and this book is an example of that. Here is a link to his webpage.
There are many other excellent introductory analysis books. Reading from other sources is always very valuable. For example: Calculus by Spivak, 4th edition Publish or Perish, 2008, or The Way of Analysis by Robert Strichartz, Jones & Bartlett Publishers, Revised Edition, 2000. For a non-standard book, but a very lively one, full of historical anecdotes, see A radical approach to real analysis by D. M. Bressoud.

Course Structure: Tuesdays and Thursdays will be devoted to lecturing on new material and occasional quizes. The additional hour on Wednesdays will be conducted by Bishnu Sedai our Teaching Assistant, and will be used for problem solving and review of the material.

Course content: This is a first course in analysis. We will cover the fundamentals of calculus in one variable, starting with the definition of the real numbers, sequences of numbers and working our way through the concepts of limits, functions, continuity and basic properties of functions, we will then study carefully the theory of differentiation and integration. Basic calculus is a prerequisite, it provides you with computational skills and some intuition. Prior experience with abstractions and proofs will be helpful (for example exposure to at least one of Math 306, 317, 318, 319, 321, 322 or 327 will provide such experience). However we do not expect the students to be able to read, understand, and actually construct mathematical proofs at the begining of the course, although most of you have probably been already exposed to this. A great amount of time will be devoted to learn and practice logical thinking. At the end of the course we expect the students to have adquired the basic skills of mathematical reasoning, and a deeper understanding of calculus.

Homework: The problems and exercises in the textbook are an integral part of the course. You should attempt most of them. Homework will be assigned periodically, the problems in the homework will be carefully graded, and returned to you with feedback that will help you correct any errors. The highlights of the solutions will be discussed in the Wednesday session. You are encouraged to discuss the homework with each other, but you should do the writing separately. You learn mathematics by doing, and there is no way around this. It is not enough to see your teacher or your friends solving problems, you have to try it yourself. Difficult as it may seem at the beginning, if you persist you will learn how to write a proper mathematical proof, you will learn how to read and understand other's proofs, and you will learn to appreciate and enjoy the beauty of an elegant argument.

Exams: There will be two midterms during weeks 6 and 12, and a final exam.

Grades: The final grade will be determined by your performance on homeworks/quizes, midterms, and a final exam. The grading policies will be discussed in class.

Prerequisites: Basic calculus: Math 162-163 and Math 264. (or permission from the instructor).

Americans with Disabilities Act: Qualified students with disabilities needing appropriate academic adjustments should contact me as soon as possible to ensure your needs are met in a timely manner. Handouts are available in alternative accessible formats upon request.

Return to: Department of Mathematics and Statistics, University of New Mexico

Last updated:January 20, 2014