Course: Math 215, Introduction to Advanced Mathematics

Call no: 42482

Time: MWF 4:00pm - 4:50pm

Place: 310 Addams Hall

Professor: Dhruv Mubayi

Office: 620 SEO

Tel:
3-8036

E-mail: mubayi@uic.edu

Course Web Page:
http://www.math.uic.edu/~mubayi/215/fall22/215Fall22.html

Office Hours: Wednesday and Friday: 1-2

Grading Policies:

Attendance and class participation: 20%

Homework, due every week: 20%

Two in-class midterms, 20% each

Final Exam: 20%

Be sure to staple your homework. No late homework will be
accepted.

Disability Policy: Students with disabilities who require accommodations for access and participation in this course must be registered with the Office of Disability Services (ODS). Please contact ODS a 312/413/-2183 (voice) or 312/413-0123 (TTY).

Prerequisite: Grade of C or better in MATH 181 and approval of the department.

Description: Introduction to methods of proofs used in different fields in mathematics.

Text: Peter J. Eccles, An introduction to Mathematical Reasoning, Cambridge University Press.

Homework

Homework 1, Due Friday Jan 23:Chapter 1: 1.2 (iii), (iv); 1.4; 1.5

Chapter 2: 2.1 (i), (ii), (x),(xi); 2.4; 2.6

Chapter 3: 3.1 (ii); 3.2; 3.4; 3.7; 3.8 (iv)

Homework 2, Due Friday Jan 30:

Chapter 4: 4.1; 4.2; 4.3; 4.6

Problems I (page 53-56): 2, 8, 9, 10, 12, 14, 19

Homework 3, Due Friday Feb 6:

Problems I: (page 53-56): 15, 16, 17, 21, 23, 25, 26

TEST 1: FRIDAY FEBRUARY 13

Homework 4, Due Friday February 20

Problems II: (page 115-119) 1 (i), 2, 3, 6, 8, 9, 11 (i), (ii), (v), (vi), (ix), (x), 12

Homework 5, Due Friday February 27

Problems II (page 115-119): 13 (ii), 15, 16 (i), (iii), (iv), (v), (vi)

Homework 6, Due Friday March 6

Problems II (page 115-119): 18, 21 (i)

Problems III (page 183-187): 8, 9, 12 (please write careful proofs)

Homework 7, Due Friday March 13

Problems III (page 183-187) 1, 6, 11, 13, 14, 15, 16, 18, 20

This homework is hard so be sure to start early and come by with questions if needed.

Homework 8, Due Friday, March 20

Problems III (page 183-187) 16 (do it again), 17, 18 (do it again), 21, 22 (show well-definedness and (i))

Homework 9, Due Friday, April 3

Problems III (page 183-187) 23, 24, 25, 26, 27, (extra credit 28)

TEST 2: WEDNESDAY APRIL 8

No homework due Friday April 10

Homework 10, Due Friday April 17

Problems IV (page 225-228) 6, 10, 13, 19

Homework 11, Due Friday April 24

Problems IV (page 225-228) 15

Problems V (page 271-273) 7,8, 10 (i) (iv), 11

Homework 12, Due Friday May 1

Problems V (page 271-273) 15 (i), 17 (i), (iv)

Problems VI (page 295-297) 2, 8, 13, 16 (i)