MA 341: Introduction to Mathematical Analysis


Course Information

Professor: Kiril Datchev
Email: kdatchev@purdue.edu
Lectures: Tuesdays and Thursdays, 10:30 to 11:45 or 12:00 to 1:15, in SCHM 123.
Office hours: Mondays 4:15-5, Thursdays 1:20-2:30, or by appointment, in MATH 602.

Grading is based on
  • Almost weekly homework assignments, worth 20% of the total grade,
  • two midterm exams, from 8 to 9 pm in ME 1130, on 2/16 and 4/6, each worth 20% of the total grade,
  • a final exam, as scheduled here, worth 40% of the total grade.

    • We will cover the following topics: real and complex numbers, infinite sequences and series, convergence, approximation, continuity, differentiation, and integration.

    Course Notes

    Introduction

    Sequences

    Continuity

    Homework

    Homework is due on paper at the beginning of class on Tuesdays. Justify your answers.

    Homework 1, due January 20th, is Exercises 2.2, 3.1, 4.2, and 4.5 from the Introduction.

    Homework 2, due January 27th, is Exercises 1.7, 2.3, 3.3, 3.6, 3.13, 3.15, 3.17 from Sequences.

    Homework 3, due February 3rd, is Exercises 4.2, 4.5, 4.6, 4.10, 4.11, 5.2, 5.7, 5.9, 5.15 from Sequences.

    Class is canceled February 12th and April 16th.

    Review problems for Midterm 1. Miscellaneous examples.

    Homework 4, due February 24th, will be posted later.

    Additional Reading

    The best modern introductory analysis textbook is Mattuck's Introduction to Analysis. It is used here.
    We will try to improve on it by following Hume's challenging principle of avoiding all unnecessary detail.

    At the opposite extreme, with an abundance of beautiful detail, is Loya's Amazing and Aesthetic Aspects of Analysis.
    It draws on many classics, most notably Euler's Introduction to Analysis of the Infinite.

    At a higher level, it is hard to beat the depth and polish of Rudin's Principles of Mathematical Analysis, although one has to dig for the motivation and context.

    The best book on the question of what is a real number is still Dedekind's Continuity and Irrational Numbers.

    Finally, a list of general policies and procedures can be found here.