Uncategorized – Corey Bacal Switzer

The following problems are for HW #3, which is due this Thursday, January 18th.

For the first three problems use $\epsilon - \delta$ to show the following limits are true.

$\lim_{x \to 1} 2x - 3 = -1$
$\lim_{x \to 2} \frac{x^2 - 4}{x-2} = 4$
$\lim_{x \to a} 3x + 2 = 3a + 2$ for all $a \in \mathbb R$ .
Prove for contradiction that the following limit does not exist: $\lim_{x \to 0} \frac{1}{x} + x^2$ .

The rest of the problems are from the textbook.

Chapter 4: 17

Chapter 5: B. 14, 15

Chapter 6: A. 6, 14

EXTRA CREDIT: Following the problem with the last homework, let me be clear that (in this class) $0$ counts as a natural number! For extra credit, give an example of a property of natural numbers $n$ that is true for all $n > 0$ but false for $n = 0$ .

Please let me know if you have any questions.

Welcome to Math 156 at Hunter College City University of New York. Here is the syllabus for the course, also available as a pdf here: Math 156 Syllabus.

MATH 156.W02 Introduction to Mathematical Proof Workshop, 2 hrs, 1 cr, Winter 2018

Meets: Monday, Tuesday, Wednesday, Thursday, 9:00am-11:05am, Room 604HW

Instructor: Corey Switzer

Office Hours: Thursdays from 11:30-12:30 in Room 924 HE, other times by appointment

Email: cswitzer[“at” sign]gradcenter[dot]cuny[dot]edu (Please include Math 156 in the subject line)

Textbook: Book of Proof, Second Edition, by Richard Hammack © 2013, Richard Hammack (publisher). ISBN 978-0-9894721-0-4, (313 pages). Download the ebook for free from the author’s website here, and/or purchase the print edition on Amazon or Barnes & Noble for around $15.

Notes: Other notes will be passed out in class and available at the course website here.

Course Learning Outcomes:

Construct direct and indirect proofs and proofs by induction and determine the appropriateness of each type in a particular setting. Analyze and critique proofs with respect to logic and correctness, and prove conjectures
Learn to construct proofs that are not only mathematically correct but also clearly written, convincing, readable, notationally consistent, and grammatically correct,
Apply the logical structure of various proof techniques, proof types, and counterexamples and work symbolically with connectives and quantifiers,
Perform set operations on finite and infinite collections of sets and be familiar with properties of set operations and different cardinalities for infinite sets,
Work with relations and functions, including surjections, injections, inverses, and bijections, equivalence relations, and equivalence classes,
Learn to work with ε–δ definitions and proofs involving limits at a point for polynomials, rational functions, as well as transcendental functions that do not have a limit at a point,

Course Content to be Covered

Syllabus: As a rough guide, we will cover most Chapters from the following:

Chapter 1: Sets
Chapter 2: Logic
Chapter 4: Direct Proof
Chapter 5: Contrapositive Proof
Chapter 6: Proof by Contradiction
Chapter 7: Proving Non-Conditional Statements
Chapter 8: Proofs Involving Sets
Chapter 9: Disproof
Chapter 10: Mathematical Induction
Chapter 11: Relations
Chapter 12: Functions
Chapter 13: Cardinality of Sets
Epsilon-Delta Proofs

General: A typical class will begin with some problems for the previous class to test comprehension. Students will be expected to work with one another on these problems and, on occasion, present solutions. Then, I will introduce topics and examples of proof techniques from the text. It is important to understand what goes on in class each day. This means being present and being prepared for every class, first by reading the textbook and second by making a serious effort to do the homework.

It is encouraged that you work together both on reviewing the material and doing the homework. However, this is not an excuse for copying some one else’s work. Every student is expected to turn in their own, original work.

Last Day to Withdraw with a Grade of W: 1/16/17

Grading/Test Dates:
Class participation (including attendance), 25%; Homework (Due roughly twice a week), 25%; Midterm (Take Home, Due 1/15), 25%; Final Exam (In Class, January 23rd), 25%

Academic Integrity:

Hunter College regards acts of academic dishonesty (e.g., plagiarism, cheating on examinations, obtaining unfair advantage, and falsification of records and official documents) as serious offenses against the values of intellectual honesty. The College is committed to enforcing the CUNY Policy on Academic Integrity and will pursue cases of academic dishonesty according to the Hunter College Academic Integrity Procedures.

Disabilities: If you have a disability that you believe requires special accommodations: In compliance with the American Disability Act of 1990 (ADA) and with Section 504 of the Rehabilitation Act of 1973, Hunter College is committed to ensuring educational parity and accommodations for all students with documented disabilities and/or medical conditions. It is recommended that all students with documented disabilities (Emotional, Medical, Physical and/or Learning) consult the Office of AccessABILITY located in Room E1124 to secure necessary academic accommodations. For further information and assistance please call (212-772-4857)/TTY(212-650-3230).

Corey Bacal Switzer

Corey Bacal Switzer

Category: Uncategorized

Final Study Guide

Homework # 3

Homework #2

Homework #1

Welcome!