This class is cross-listed as:
Textbook: Analysis with an introduction to proof. by Steven R. Lay (required). There are many other excellent introductory analysis books. Reading from other sources could be very valuable.
Course Structure: There are 3 lectures per week. The course will cover most of the material in Chapter 1-7 of our book. It is very helpful to read the material before it is discussed in class. Here is a tentative syllabus (pdf) we might have to adjust it as we go along. Here is an updated syllabus (pdf). Tuesdays and Thursdays will be devoted to lecturing new material. The additional hour (Fridays at 11am) 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. 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, plus a deeper understanding of calculus.
Homework: Homeworks will be assigned periodically. 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 begining, 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 take home final exam. Here is the review for the first exam: Review #1 (pdf), and the solutions. Here is the review for the second exam: Review #2 (pdf), and the solutions will be posted soon.
Grades: The final grade will be determined by your performance on homeworks, midterms, and 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: Nov 6, 2001