Math 214-01: Foundations of Mathematics (Spring 2022)
- Instructor: Junping Shi, Jones 100B, phone:
221-2030, jxshix@wm.edu
- Meeting time and location:
Tuesday and Thursday 11:00-12:20, Boswell
Hall 201
- Web pages:
- Office Hours: TR 14:00-15:15pm or by appointment.
- Add/drop deadline: Feb 4, Withdraw deadline: March 28
- 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 March 10 (Thursday) and
April 21 (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 test.
- Final Exam: A comprehensive final exam will be
held on Tuesday
May 10, 2-5pm. Location: Boswell Hall 201
- 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: This semester, the world
will enter its third year with COVID. As we experience a fifth surge of
pandemic with the highly transmissible omicron variant, it is reasonable
to expect significant levels of infection at W&M. As an academic
community based on faculty and students convening, Spring 2022
courses will largely consist of in-person instruction. All of us will
follow W&M requirements - vaccinations and boosters, indoor masking,
as well as quarantine and isolation when ill. That last is really
important: for those who have tested positive, W&M’s requirements must
be fulfilled before class can be attended in person, and, out of an
abundance of caution, anyone with symptoms consistent with COVID- even if
they don’t have a positive test- should not come to class.
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.
Consistent
with W&M’s belief that learning is most effective when the instructor and
students convene, our course this semester is scheduled for in-person
instruction. That said, we are still dealing with a pandemic, even as it ebbs
toward an endemic. In this setting, we need to have a way to communicate when
students or the instructor cannot be in person. 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. Since this is a very challenging
time with the potential for quite complicated comings and goings, we need to
operate on the basis of a trustful relationship; please try your very best not
to miss classes for non-health related reasons.
For this course in Spring 2022, here is the way that we will
address student absences: (i) Share
Instructor’s notes for class; (ii) Create a contact system so that students who
have missed class have an assigned group of classmates to reach out to in order
to learn about the class(es) missed; and here is the way we will address instructor absence: the
Instructor converts classes to zoom on a temporary basis.
- 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