
Professor Alexandru I. Suciu


MATH 3150 · Real Analysis

Fall 2016

Course Information
Course

MATH 3150 · Real Analysis

Instructor

Alex Suciu

Course Web Site

www.northeastern.edu/suciu/MATH3150/analysis.fa16.html

Time and Place

Monday & Wednesday 2:50pm4:30pm, in 266 Ryder Hall

Office

435 LA – Lake Hall

Phone

(617) 3733899

Email

a.suciu@neu.edu

Office Hours

Monday & Wednesday 4:405:40pm or by appointment, in 435 Lake Hall

Prerequisites

MATH 2321 (Calculus 3 for Science and Engineering) and MATH 2331 (Linear Algebra)

Textbook

An Introduction to Classical Real Analysis,
Karl R. Stromberg, AMS Chelsea Publishing, 2015

Course Description

Provides the theoretical underpinnings of calculus and the advanced study of functions. Emphasis is on precise definitions and rigorous proof. Topics include the real numbers and completeness, continuity and differentiability, the Riemann integral, the fundamental theorem of calculus, inverse function and implicit function theorems, and limits and convergence.

Grade

Based on problem sets (40%), midterm exam (20%), and final exam (40%). It is expected that you will work on the problem sets together; however, they must be written up separately.


Homework assignments

Homework 1: Chapter 1, Problems 6, 10, 18, 23, 25, and one more: Given two subsets A, B of R, show that
inf(A+B) = inf(A)+inf(B), where A+B={a+b : a ∈ A and b ∈ B}.
Due Monday, September 19. Solutions to Homework 1

Homework 2: Chapter 2 (pp. 8486): Problems 2(b)(c), 7, 8, 15, 18(b). Due Monday, October 3.
Solutions to Homework 2.

Homework 3: Chapter 2 (pp. 8687): Problems 21, 24, 28 and Chapter 3 (p. 111): Problems 2, 3. Due Wednesday, October 19.

Homework 4: Chapter 3 (pp. 119121): Problem 1 (for f_1 and f_2 with S_1, S_2, S_4,
only compute the limits, not the iterated limits), Problems 6 and 8; and Chapter 3 (pp. 124125): Problems 9 and 17. Due Monday, November 7.

Homework 5: Chapter 3 (pp. 111113): Problems 4, 14, 16; (p. 120): Problem 2; (p. 124): Problem 1. Due Wednesday, November 16.

Homework 6: Chapter 3 (p. 144): Problems 1(ab), 2, 4; Show that the sequence in Example (3.111)(d) is NOT uniformly convergent; Chapter 4 (p. 183): Problem 4. Due Wednesday, November 30.
Solutions to Homework 6.

Homework 7: Chapter 4 (pp. 183187): Problems 5, 17, 21 (a,e,i); (p. 198): Problem 3 (a,b); (p. 215): Problem 2. Due Friday, December 10.
Course Materials and Exams

Review session: Monday December 12, from 3:00pm to 5:00pm, in 509 Lake Hall.

Final exam: Wednesday December 14, at 3:305:30pm, in Hastings Suite 104.
