Math 214-01 (Spring 2022) Schedule (subject to change)

LaTeX is a programming language to type texts with math content. You need to use some text editor to compile your .tex file, then use a latex compiler to typeset your latex file.

Date

Sections

Lecture  Notes

Homework

Other readings

1/27(R)

0, 1.1-1.2

Lecture1
math major Writing

 

The Grammar According to West

2/1(T)

1.3-1.6

Lecture2

Homework 1 (tex, pdf) (due 2/4 F)
Optional additional problems (do not turn in)
Chap1(3,5,9,21,25,33,37,51,63,67)

set set of all sets partition of set

2/3(R)

2.1-2.9

Lecture3

de Morgan's law
double negative Exclusive Or Incusive or

2/8(T)

2.1-2.10, 7.2

Lecture4

Homework 2 (tex, pdf) (due 2/11 F)
Optional additional problems (do not turn in)
Chap2(9,23,25,27,31b,33c,39c,53,57,69,71,79)

Knights and Knaves

2/10(R)

2.1-2.10, 7.2, 3.1-3.3

Lecture5

Notes 1

Bell number

2/15(T)

3.3-3.4

Lecture6

Homework 3 (tex, pdf) (due 2/18 F)
Optional additional problems (do not turn in)
Chap3: (21,37,51,65)

Most beautiful theorems
Fermat's theorem on sums of two squares
Fermat's Last Theorem
 

2/17(R)

4.1, 4.3

Lecture7

prime number
Goldbach conjecture Green-Tao Theorem
Twin prime conjecture
Notes 1

2/22(T)

4.1-5.5

Lecture8

Homework 4 (tex, pdf) (due 2/25 F)
Optional additional problems (do not turn in)
Chap 4: (27,31,39,81,95) Chap 5:(11,17,19,29,49,51,55)

Putnam competition
Virginia Tech Competition

Reductio ad absurdum

2/24(R)

6.1-6.2

Lecture9

Mathematical induction

3/1(T)

6.2-6.3

Lecture10

Homework 5 (tex, pdf) (due 3/4 F)
Optional additional problems (do not turn in)
Chap 6: (1,5,9,15,21,25,31,39,49)

an MI notes
All horses are the same color paradox
Srinivasa Ramanujan

3/3(R)

6.3, 12.1-12.4

Lecture11

Cauchy-Schwarz inequality
AM-GM inequality
Tower of Hanoi

3/8(T)

12.3-12.4

Lecture 12


3/10(R)

Exam 1

Homework 6 (tex, pdf) (due 3/25 F)
Optional additional problems (do not turn in)
Chap 12: (7,21,27,35,37c,38c,41,49,55,63c)

Euclidean algorithm
Relatively prime numbers

3/11-19

Spring Break

no class

 

Date

Sections

Lecture Notes

Homework

Other readings

3/22(T)

12.5-12.6

Lecture13

3/24(R)

12.6, 4.2

Lecture14

Homework 7 (tex, pdf) (due 4/1 F)
Optional additional problems (do not turn in)Chap 12: (65,81,87) Chap 9(3,7,9,19,23)

divisibility
Last digit

3/29(T)

9.1-9.3

Lecture15

modular arithmetic

3/31(R)

9.4-9.5

Lecture16

Homework 8 (tex,pdf) (due 4/8 F)
Optional additional problems (do not turn in)Chap 9: (25,33,41,49,51)

From Terry Tao's blog 1
From Terry Tao's blog 2

4/5(T)

9.6, 10.1-10.2

Lecture17

permutation

4/7(R)

10.3

Lecture18

Homework 9 (tex, pdf) (due 4/15 F)
Optional additional problems (do not turn in)Chap 9: (61,71) Chap 10 (3,7,9b,27,33,37,45,53,55,59,67c,71)

Equivalence relation

4/12(T)

10.4

Lecture19

Bijection

4/14(R)

10.5

Lecture20

Injection
Surjection

4/19 (T)

11.1-11.2

Lecture21

Exam 2 Review and sample problems

4/21(R)

Exam 2

4/26 (T)

11.1-11.2

Lecture22

Homework 10 (tex, pdf) (due 4/29 F)
Optional additional problems (do not turn in) Chap 11 (5,7,9,17)

cardinal numbers
Hilbert's grand hotel (video)
Georg Cantor  Cantor's diagonal argument

4/28(R)

11.3

Lecture23

0.999.... Cantor pairing

5/3 (T)

11.4-11.5

Lecture24

Homework 11 (tex, pdf) (due 5/6 F)

Optional additional problems (do not turn in) Chap 11 (26,33,35,41,49,51)

continuum hypothesis

Bernstein–Schroeder theorem
space-filling curve  

5/5(R)

11.4-11.5

Lecture25

Final exam review

Final Notes
Sample Final exam Spring 2014 Spring 2016

5/10(T)

Final Exam 2-5pm

Some Mathematics Pop Books