Math
214-03: Foundations of Mathematics (Fall 2022)
- Instructor: Junping Shi, Jones 117, phone:
221-2030, jxshix@wm.edu
- Meeting time and location:
Tuesday and Thursday 11:00-12:20, Boswell
Hall 40
- Web pages:
- Office Hours: WR 15:30-17:00pm or by appointment.
- Add/drop deadline: September 12
(Monday), Withdraw
deadline: October 31 (Monday)
- Text: Mathematical Proofs--A Transition to Advanced Mathematics
by Gary Chartrand, Albert D. Polilmeni, and Ping
Zhang (Fourth Edition). ISBN-13: 978-0134746753.
- 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)
- Exams: There will be two mid-term exams (80 min each) on October 11 (Tuesday) and
November 17 (Thursday). Make-up 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 exam.
- Final Exam: A comprehensive final exam will be
held on Friday
December 16, 2-5pm. Location: Boswell Hall 40
- 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 will be assigned and submitted through Gradescope (access from Blackboard site). It is
usually due Friday midnight. Two lowest homework scores will be dropped.
You are encouraged to discuss homework with other people, but you must
write up the homework by yourself. Selected problems will be graded, but
completeness will be checked.
- LaTeX: You are required 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.
- Calculators: Electrical calculators are not
allowed in midterm and final exams.
- Attendance: Students are expected to attend
lectures in the classroom if you are not sick. But if a student is tested
positive for COVID-19 or has other temporary illness, the student needs to isolate and not attend in-person
classes for at least five days. As soon as a student knows they will not
be able to attend class in person (either because of having tested
positive, having symptoms consistent with COVID, or other health matters),
please email the instructor. In that case, the instructor will activate
our mode of accommodating absences for your situation. Lecture notes of
all classes will be shared with students, and if there is a group of
students cannot attend classes, the instructor may use Zoom to broadcast
classes from the classroom on a temporary basis.
Please note that testing positive for COVID or any other temporary
illness is not considered a disability as defined by ADA guidelines and is not
under the purview of W&M’s Student Accessibility Services (SAS). Thus, any
questions should be addressed via email to the instructor.
- Grading: Your final grade is calculated as follows: Homework 40%
(4% each); Mid-term Exams 30% (15% each); Final Exam: 30%. 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: William & Mary has had an honor code since at least
1779. Academic integrity is at the heart of the university, and we all are
responsible for upholding the ideals of honor and integrity. The
student-led honor system is responsible for resolving any suspected
violations of the Honor Code, and I will report all suspected instances of
academic dishonesty to the honor system. The Student Handbook (www.wm.edu/studenthandbook)
includes your responsibilities as a student and the full Code. Your full
participation and observance of the Honor Code is expected. To read the
Honor Code, see www.wm.edu/honor
- ADA accommodation: William & Mary accommodates students with
disabilities in accordance with federal laws and university policy. Any
student who feels s/he may need an accommodation based on the impact of a
learning, psychiatric, physical, or chronic health diagnosis should
contact Student Accessibility Services staff at 757-221-2509 or at
sas@wm.edu to determine if accommodations are warranted and to obtain an
official letter of accommodation. For more information, please see http://www.wm.edu/sas
- Mental and Physical Well-Being: William & Mary recognizes that students juggle
different responsibilities and can face challenges that make learning
difficult. There are many resources available at W&M to help
students navigate emotional/psychological, physical/medical,
material/accessibility concerns. Asking for help is a sign of courage and
strength. If you or someone you know is experiencing any of
these challenges, we encourage you to reach out to the following offices:
·
For
psychological/emotional stress, please consider reaching out to the W&M
Counseling Center https://www.wm.edu/offices/wellness/counselingcenter/; or
(757) 221-3620, 240 Gooch Dr., 2nd floor. Services
are free and confidential.
·
For
physical/medical concerns, please consider reaching out to the W&M Health
Center at https://www.wm.edu/offices/wellness/healthcenter/;
or (757) 221-4386, 240 Gooch Drive.
·
For
additional support or resources, please contact the Dean of Students by
submitting a Care Report at https://www.wm.edu/offices/deanofstudents/services/caresupportservices/index.php;
or by calling 757-221-2510, or by emailing deanofstudents@wm.edu.
·
For
a list of many other resources available to students, see Health
and Wellness Resources for Students