Math 214

Math 214-01: Foundations of Mathematics (Spring 2023)

Instructor: Junping Shi, Jones 117, phone: 757-221-2030, jxshix@wm.edu

Meeting time and location: Tuesday and Thursday 9:30-10:50, Jones Hall 306

Web page: Blackboard link

Office Hours: TR 14:00-15:20pm or by appointment.

Add/drop deadline: Feb 3, Withdraw deadline: March 27

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 7 (Tuesday) and April 18 (Tuesday). 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 Thursday May 11, 9-12am. Location: Jones Hall 306

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: Attendance of classes is required. If you have any illness and other situations preventing you from attending classes, you should notify the instructor before the class. The student is responsible for acquiring class notes for any missed lectures (instructor will post lecture notes on Blackboard but it may be slightly different from the class ones)

Grading: Your final grade is calculated as follows: Homework 40%; 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, including:

· The W&M Counseling Center at (757) 221-3620. Services are free and confidential.

· The W&M Health Center at (757) 221-4386.

· For additional support or resources & questions, contact the Dean of Students at (757) 221-2510.

· For other resources available to students, see https://tinyurl.com/wmmentalhealth