MA 504 Spring 2025

Instructor	Plamen Stefanov
Office	MATH 728
Email	stefanov@math.purdue.edu
Meeting	TueThu 9:00 - 10:15 in SCHM 123
Office Hours	TueThu 1:00-2:00
Grader	Vicente Loccada
Book	Walter Rudin, Principles of Mathematical Analysis (3rd Edition)

Homework

HW1: p.21-22: 2, 4, 5, 8. Due Jan. 26 (Sun)

HW2: p.43: 2, 3, 4, 5, S1 Due Feb. 2 (Sun)

HW3: p.43: 11, 12, 14, 16, 22, 29. Due Feb. 9 (Sun)

HW4: p.78: 1, 2, 3, 6, 7, 8, S2. Due March 2 (Sun)

HW5: p.78-82: 9, 16, 20. Due March. 9 (Sun)

HW6: p.98-102: 2, 3, 4, 7, 14, 15. Due March. 25 (Tue)

HW7: S3, due March 31 (Mon)

HW8: p.114: 1, 2, 3, 4. Due April 13 (Sun)

HW9: p.138: 1, 2, 4, 5, 7, 8, 11. Due April 20 (Sun)

HW10: p.165: 1, 2, 4, 6, 9, 20. Will not be collected .

Exam 1: Thursday, Feb. 13, in class.

What I skipped: a more formal discussion on complex numbers (pp.12-15); cells, Cantor sets (because we are not covering measure in this course), connected sets.
Practice questions
The rules have been relaxed: Aside from the book or printed pages from it, you can use unlimited number of notes, including the ones you took in class. No other books or printed pages from other sourses, like from other books, online materials, etc. No electronic devices of any sort.

Exam 2: Thursday, April 3, in class.

Will cover Chapters 4 but then this chapter depends on the other three as well.
Same rules as before.
What I skipped: connectedness.

Final exam: Thu 05/08, 3:30p - 5:30p, KRAN G018

Will cover the whole material (which I covered in class). In particular, sequences and series, including uniform convergence, will be on the exam.
Same rules as before.
Practice questions

Course grade

Your course grade will be determined using the following distribution: HW: 1/3; Midterm 1/6 each (1/3 total); Final: 1/3.

Schedule

SCHEDULE (Tentative)

Chapter 1: The Real and Complex Number System
    Real number system
    Extended real number system
    Euclidean space

Chapter 2: Basic Topology
    Finite, Countable and Uncountable sets
    Metric spaces (a few examples)
    Compact sets

Chapter 3: Numerical Sequences and Series
    Convergent sequences
    Subsequences
    Cauchy sequences
    lim-sup and lim-inf
    Series
    Absolute and conditional convergence
    Rearrangements

Chapter 4: Continuity
    Limits of functions
    Continuous Functions
    Continuity and compactness
    Intermediate Value Theorem
    Monotone Functions (limits, discontinuities)

Chapter 5: Differentiation
   The derivative
   Mean Value Theorem
    Continuity of derivatives
    Intermediate Value Theorem
    Derivatives of higher order
    Taylor's Theorem
    Derivatives of vector-valued functions

Chapter 6: The Riemann-Stieltjes Integral
    Definition and Existence
    Properties
    Integration and Differentiation

Chapter 7: Sequences and Series of Functions
    Uniform convergence
    Uniform convergence and Continuity
    Uniform convergence and Integration
    Uniform convergence and Differentiation
    Eigencontinuous families of functions
    Stone–Weierstrass Theorem

Chapter 8: Some Special Functions
    Power series
    exp and log
    sin and cos