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MATH 30800-R, Bridge to Advanced Mathematics

### Instructor and Course Information:

Instructor: Sergiy Merenkov

Email: smerenkov@ccny.cuny.edu

Office: NAC 6/280

Time: TuTh: 03:30PM-04:45PM

Room: NAC 6/111

Office Hours: by appointment

Textbooks:

Elementary Analysis: The Theory of Calculus, Author: Ross, Kenneth A., Publisher: Springer, Edition: 2, Year Published: 2013

Mathematical Proofs: A Transition to Advanced Mathematics, Author: Chartrand, Gary, Polimeni, Alb, Publisher: Pearson, Edition: 3, Year Published: 2012

An Introduction to Proofs and the Mathematical Vernacular, by Martin Day

Course Description and Syllabus

Midterm 1: Tu 10/03, in class, 25%

Covers: system of natural numbers, induction principle.

Midterm 2: Tu 11/07, in class, 25%

Covers: relations, equivalence relations, systems of integers and rationals, order.

Final Exam: Tu 12/19, 03:30PM-05:45PM, in classroom, 40%

Covers: everything covered by Midterms 1 and 2, and, in addition, irrationality of square root of 2, quantifiers, negation, compound mathematical statements, logical equivalence, sequences, limit, Cauchy sequences, subsequences, real numbers, completeness axiom.

Homework: 10%

### Assignments:

HW 1 (due 09/14, in class).

HW 2 Do the following problems from Mathematical Proofs: A Transition to Advanced Mathematics, Author: Chartrand, Gary, Polimeni, Alb, Publisher: Pearson, Edition: 3, Year Published: 2012: ## 6.4(1), 6.6(b), 6.48 (due 09/28, in class).

HW 3 Do the following problems from Mathematical Proofs: A Transition to Advanced Mathematics, Author: Chartrand, Gary, Polimeni, Alb, Publisher: Pearson, Edition: 3, Year Published: 2012: ## 8.12, 8.28, 8.40 (due 10/12, in class).

HW 4 (due 11/02, in class).

HW 5 (due 12/05, in class).