Math 108, Fall 2017: Introduction to Abstract Mathematics
In this course we introduce the rigorous foundations of abstract mathematics. In particular, we will cover formal logic and natural deduction, methods of proof such as induction and contradiction in practice, set theory and functions, bijections and cardinality, combinatorial proofs, and the basics of abstract algebra (groups, rings, and fields).
For more information, see the Course Syllabus.
The textbook for the course is A Transition to Advanced Mathematics, 8th Ed., by Eggen, Smith, St. Andre. However, the course will also be following some of the material in the following lecture notes:
Homework
Homework 1 - Due Oct. 2
Homework 2 - Due Oct. 9
Homework 3 - Due Oct. 16
Homework 4 - Due Oct. 23
Homework 5 - Not handed in; study for Midterm 1!
Homework 6 - Due Nov. 6
Homework 7 - Due Nov. 13
Homework 8 - Due Nov. 20
Homework 9 - Due Nov. 27
Homework 10 - Due Dec. 4
Exams
There will be one midterm on October 30, and a final exam. See the syllabus for more details, and check back here for practice problems as the exam dates approach.
Final exam schedule
Section A01 (11am class): Thursday, Dec. 14, 10:30am-12:30pm, Haring 2016
Section A02 (11am class): Thursday, Dec. 14, 10:30am-12:30pm, Haring 1204
Sections C01, C02 (3pm class): Wednesday, Dec. 13, 8:00am-10:00am, Everson 176
Projects
In lieu of a second midterm exam, there will be a written project, designed to give you practice thinking about a difficult mathematical problem for a longer period of time, and to give you feedback on your expository mathematical writing. The project will consist of a mathematical investigation starting from any one of the provided prompt problems in the document below. See the prompts file for more instructions and details:
In order to type your solutions in LaTeX, the easiest way to start is to get a free account on Overleaf.com, an easy-to-use browser-based LaTeX editor. You can then either start your document from scratch, or make your own copy of any of the following example documents:
Simple definition/theorem/proof from Oct. 2 class
The Project Template above gives an idea of how you should organize your project.