Spring 2024 - MATH 292 D100
Selected Topics in Mathematics (3)
Class Number: 6248
Delivery Method: In Person
Overview
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Course Times + Location:
Jan 8 – Apr 12, 2024: Mon, Wed, Fri, 9:30–10:20 a.m.
Burnaby -
Exam Times + Location:
Apr 24, 2024
Wed, 3:30–6:30 p.m.
Burnaby
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Instructor:
Joanna Niezen
jniezen@sfu.ca
1 778 782-4849
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Prerequisites:
Prerequisites will be specified according to the particular topic or topics offered.
Description
CALENDAR DESCRIPTION:
Topics will vary from term to term depending on faculty availability and student interest.
COURSE DETAILS:
An important part of mathematics research is to investigate and discover patterns, and then prove the patterns hold in all cases. This course introduces students to these important skills. By studying mathematical logic, methods of argument, and the foundations of mathematics, students will gain a better understanding of what it means to prove things and how to do so rigorously – whether you have never proved anything before, or you have encountered proofs in another course. Any students who would like to bolster their proof techniques and problem-solving skills are encouraged to take this course.
This course may be used as a prerequisite for any MATH or MACM courses which typically require MACM101 as a prerequisite. This course and MACM101 contain some initial overlap but diverge in content as this course focuses on mathematical proofs, examples, and applications to help prepare you for future courses as a mathematics major or minor. Students who have taken MACM101 before are welcome to take this course to delve deeper into proofs and proof techniques.
In trying to discover the underlying structure and truth, students should expect their problem-solving skills to improve. Important, useful, non-subject-specific analysis and communication skills are developed in this class. When reading technical materials, newspaper articles, financial reports, legal documents, etc., it can be crucial to understand precisely what is and is not being said. In careers ranging from business to journalism to law to science, a person must be able to produce and communicate persuasive logical arguments.
Prerequisites: one of Math 150, 151, 154, 157 with a minimum grade of C-
COURSE-LEVEL EDUCATIONAL GOALS:
- Propositional logic, tautologies and contradictions, quantifiers, necessary and sufficient conditions, valid arguments and rules of inference.
- Set theory and proofs.
- Number theory, prime numbers, proof of infinitely many primes, modular arithmetic and congruence proofs.
- Induction and number theory applications.
- Relations, functions, and bijections.
- Cardinality proofs and different sizes of infinity.
- Introduction to group theory.
- Introduction to analysis (time permitting).
Grading
- In-class assignments and participation 10%
- Written assignments 10%
- Four 25-minute tests 40%
- Final exam 40%
Materials
REQUIRED READING NOTES:
Your personalized Course Material list, including digital and physical textbooks, are available through the SFU Bookstore website by simply entering your Computing ID at: shop.sfu.ca/course-materials/my-personalized-course-materials.
Registrar Notes:
ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS
SFU’s Academic Integrity website http://www.sfu.ca/students/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating. Check out the site for more information and videos that help explain the issues in plain English.
Each student is responsible for his or her conduct as it affects the university community. Academic dishonesty, in whatever form, is ultimately destructive of the values of the university. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the university. http://www.sfu.ca/policies/gazette/student/s10-01.html