Course Information
Course description: The goals of this course are for you to
become adept at logical reasoning by learning mathematical processes
that are essential for studying higher mathematics. We will focus
especially on the idea of a mathematical proof. We will learn how to
(1) understand mathematics in its
three modes of communication -
hearing, reading and writing, and (2) discover mathematics by exploration
and experimentation. You will have succeeded in this course if by the
end of the semester you understand or have learned
- properties of sets, integers, functions, proof by
induction, relations and partitions covered in class
- existential and
universal quantifiers; translating between English and symbolic
sentences using quantifiers
- if-then statements: when they are true,
what they are saying / not saying, what constitutes a counterexample
- how the appearance of quantifiers in the conclusion of an if-then
statement guides the structure of its proof
- how to think deeply,
carefully, and logically about new concepts
- how to explore a
concept, formulate your own questions about the concept as a result of
your exploration, and use proof techniques to prove or disprove these
questions with certainty
- how to express your ideas clearly, both
in English and using the language of mathematics
Prerequisite MTH 232.
Text Book and Syllabus: Fendel and Resek,
Foundations of Higher Mathematics , Pearson ISBN 9780201125870. We will cover Chapters 1 to 6 from the text book. See
below for a tentative list of topics by dates for this semester.
The first 6 chapters of the textbook will be supplied to
students on first day of classes. Please note that you
may not distribute, photocopy any parts of this material at any time,
and students have to return the textbook at the end of the semester.
Please bring the textbook to every class.
Attendance and class participation:
- Attendance for classes is very important and
mandatory. Students are allowed 3 excused absences.
- Class participation in form of in-class interaction and group work is important.
Homework, Quizzes and Exams Practising the concepts learned in the class and their assessment will be in the following ways:
- Homework will be assigned in most weeks in form of
reading and hand-in problems. Quizzes will be based on homework problems.
- Quizzes will usually be held at end of every chapter usually on Wednesday. Quizzes are announced on the course schedule. Additional quizzes, if any, will be announced a week in advance.
- Exams: There will be one midterm exam during the semester and
a Final exam at the end of the semester.
Here are the tentative dates (any changes will be announced well in advance)
- Midterm Exam: Wednesday Oct 28th, Review: Monday Oct 26th
- Final Exam: TBA
Grading: The course grade will determined as follows:
- Midterm Exam - approximately 25% each exam
- Final Exam - approximately 40%
- Homeworks and Quizzes - approximately 30 %
- Attendance and class participation - 5%
