Math 401/501 - Advanced Calculus I

MATH 401/501 - Avanced Calculus I
Spring 2009

This class is cross-listed as:

Textbook: Analysis I, by Terence Tao. Text and Readings in Mathematics 37. Hindustan Book Agency 2006. (required). Here you will find the first four chapter of Tao's book in pdf format pdf file. Here is Tao's page with errata. 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.
Terence Tao is an exceptional mathematician who earned in 2006 the Fields Medal, like a Novel Price in Mathematics. He also cares deeply about teaching, and this book is an example of that. Here is a link to his webpage.

Course Structure: There are 3 lectures per week. Tuesdays and Thursdays will be devoted to lecturing new material. The additional hour (Wednesdays at noon) will be conducted by Justin Pati, and will be used for problem solving and, occasionally, 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 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. 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 solve all of them. Their solutions will be discussed in the Wednesday session. Homework will be assigned periodically, the problems in the homework will be carefully graded, and return to you with feedback that will help you correct any errors. 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 it, 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. Midterm 1 scheduled on Thursday February 26, 2009. Takehome Midterm 2 due on Tuesday April 21, 2009. Here are some Review problems for chapters 9 and 10.

Grades: The final grade will be determined by your performance on homeworks, 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: Jan 8, 2009