Course code	MMAT5510
Title	Foundation of Advanced Mathematics
Lecturer	Dr. Liu Chun Lung (Kelvin) Office Rm 202A, LSB Office number 3943 7969 Email clliu@math.cuhk.edu.hk
Teaching assistants	Name Email Dr. Lin Chenran chenranlin@cuhk.edu.hk Wei Yunsong yswei@math.cuhk.edu.hk
Language	English
Lectures	YIA LT4 (Yasumoto Int'l Acad Park) 18:30 - 21:15 on Tuesdays (3/9, 10/9, 17/9, 24/9, 8/10, 15/10, 22/10, 29/10, 5/11, 12/11, 19/11, 26/11, 3/12)

The course is intended to build a solid foundation for the students on the essential topics and the rigorous reasoning of mathematics. It includes the discussion of logic, sets and functions, cardinality and countability, basic number theory, real number and limits. (Not for undergraduate students, students in the MSc. Programme in Mathematics, and students who have taken MAT/MATH5011, 5012, 5031, 5032, 5051, 570S, 6xxx and 7xxx.)

1. Sets	References: R1-Ch1, R3-Ch1, R8-Ch1,3, R10-Ch3, R11-Ch11, R12-Ch0, R13-Ch2, R14-Ch1, R15-Ch1, R17-Ch1, R18-Ch1, R19-Ch1
2. Logic	References: R1-Ch2,4-10, R8-Ch5, R11-Ch11,12, R18-Ch1, R19-Ch1
3. Relations	References: R1-Ch11, R3-Ch2, R8-Ch4, R12-Ch0, R13-Ch2, R15-Ch1, R17-Ch1, R19-Ch2
4. Functions	References: R1-Ch12, R3-Ch3, R8-Ch2, R10-Ch3, R11-Ch11, R12-Ch0, R13-Ch3, R14-Ch1, R15-Ch1, R18-Ch1, R19-Ch1
5. Number systems	References: R2-Ch1-5, R4, R5-Ch2, R6-Ch1, R7-Ch2, R8-Ch23,24, R10-Ch2,4,5, R11-Ch2,4, R12-Ch1, R13-Ch6,7,13, R15-Ch2, R17-Ch1, R19-Ch2,3
6. Number theory	References: R8-Ch10
7. Cardinality	References: R1-Ch14, R8-Ch7, R9-Ch7, R12-Ch0, R14-Ch1, R15-Ch1, R18-Ch1
8. Limits	References: R1-Ch13, R8-Ch27, R15-Ch4, R16-Ch3, R17-Ch4, R18-Ch4, R19-Ch9

1. Book of Proof (Third Edition) by Richard Hammack
2. From Natural Numbers to Quaternions by Jürg Kramer, Anna-Maria von Pippich
3. Sets, Relations, Functions by Ivo Düntsch, Günther Gediga
4. Making up Numbers A History of Invention in Mathematics by EKKEHARD KOPP
5. Constructions of the real numbers a set theoretical approach by Lothar Sebastian Krapp
6. Number Theory and Cryptography by Christian Lomp
7. Complex Analysis with Applications in Science and Engineering by Harold Cohen
8. A Comprehensive Textbook of CLASSICAL MATHEMATICS A Contemporary Interpretation by H.B. Griffiths, P.J. Hilton
9. A Comprehensive Textbook on Metric Spaces by Surinder Pal Singh Kainth
10. Analysis I by Terence Tao
11. Bridging the Gap to University Mathematics by Edward Hurst , Martin Gould
12. Elements of Mathematics by Gabor Toth
13. Essential Mathematics for Undergraduates by Simon G. Chiossi
14. Essential Real Analysis by Michael Field
15. Fundamentals of Analysis with Applications by Atul Kumar Razdan , V. Ravichandran
16. Mastering Calculus through Practice by Bárbara de Holanda Maia Teixeira, Edmundo Capelas de Oliveira
17. Real Analysis and Applications by Fabio Silva Botelho
18. Real Analysis for the Undergraduate by Matthew A. Pons
19. The Big Book of Real Analysis by Syafiq Johar

Homeworks (total will be multiplied by 1.2, but ceiling at 10%)	10%
Midterm exam will be given on Oct. 15, 18:30 - 21:15	40%
Final exam will be given on Dec. 10, 18:30 - 21:15	50%

The Chinese University of Hong Kong places very high importance on honesty in academic work submitted by students, and adopts a policy of zero tolerance on cheating and plagiarism. Any related offence will lead to disciplinary action including termination of studies at the University.

Although cases of cheating or plagiarism are rare at the University, everyone should make himself/herself familiar with the content of the following website:
http://www.cuhk.edu.hk/policy/academichonesty/
and thereby help avoid any practice that would not be acceptable.