Office Hours: TWR 14:00-15:15pm or by appointment.
Text: Mathematical Proofs--A Transition to Advanced
Mathematics by Gary Chartrand, Albert D. Polilmeni, and Ping
Zhang (Third Edition). ISBN-13: 978-0321797094.
Course goal: The primary goal is to learn how to read
and write rigorous and sophisticated mathematical statements and
proofs. An integral part of this goal is mastering mathematical
fundamentals such as logic, sets, functions, relations and
numbers. Examples and problems are drawn in such a way to survey
some different branches of "higher" mathematics.
Content: sets. logic, methods of proof (direct,
contrapositive, cases, steps, contradiction), mathematical
induction, integers, real numbers, congruence, equivalence
relations, modulo arithmetic, function, injective/surjective
functions, cardinalities of sets, countable/uncountable sets,
basic number theory (division algorithm, greatest common
divisor, Euclidean algorithm, relatively prime, fundamental
theorem of arithmetic)
Quizzes and Tests: There will be Four (20 min) quizzes
on Sept 8, Sept 22, Oct 27, Nov 29. There will be Two
mid-term exams (80 min) on Oct 4 (Tuesday) and November 15
(Tuesday). Make-up quizzes or tests are only given in
extreme circumstances such as documented serious illness or
personal circumstance. I must review such cases prior to
the start of the test.
Final Exam: final exam will be held on Tuesday
December 6, 9am-12noon. Location: Integrated Science
Add/drop deadline: Sept 2, Withdraw deadline:
Homework: There will be weekly homework assignments. We
cannot emphasize the importance of homework enough. Although
understanding material while you read the text or listen to
lecture is certainly important, your most important studying
will be in completing the homework assignments. Perhaps the most
fundamental part of this course is learning how to write and
read precise mathematical ideas. Part of writing precise
mathematical ideas is writing complete sentences with correct
grammar. Homework written incoherently will not be judged
complete! Incoherently includes, but is not limited to, using
incomplete sentences, using incorrect grammar and overusing
unnecessary mathematical notation. You are STRONGLY encouraged
to discuss your homework with us prior to handing in homework.
Start homework early and work steadily! Homework is usually due
5pm Friday, and a hard copy should be turned in to Jones 117. You are strongly suggested to use
LaTeX to type your homework. 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. Two lowest homework scores will be
Group Study/Help Session: A weekly homework group
study/help session will be offered every Thursday at Jones Hall
131. Time: 14:00-15:00pm
Calculators: Electrical calculators are forbidden in
quizzes and exams.
Attendance: Regular attendance is critical for your
success in this course. I expect your presence at every lecture.
Grading: Your final grade is calculated as follows:
Quizzes 16% (4% each)
Homework 20% (2% each)
Mid-term Exams 32% (16% each)
Final Exam: 32%
The letter grade is assigned using the scale:
A > 93 > A- > 90 > B+ > 87 > B > 83
> B- > 80> C+ > 77 > C > 73 > C- >
70 > D+ > 67 > D > 63 > D- > 60 > F
Honor Code: Students will uphold William and Mary's
stated honor code as it is written, any infractions will be
referred to the Honor Council.