215 - Introduction to advanced mathematics - Fall 2017 - UIC

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Section 28001.
Time: 12:00-12:50pm MWF.
Place: Taft Hall (AH) 308.

E-mail: benjamin.antieau@gmail.com.
Course webpage: dantie1.people.uic.edu/201703-215.html.

Office hours: 11am-12pm MF in SEO 419.

Book: Peter Eccles, An introduction to mathematical reasoning, any version.

Course objectives: to gain mathematical maturity; to gain skill and self-confidence by learning to construct, modify, check, discuss, write, edit, summarize, present, and critique proofs and counter-examples; to continue developing from being "solution imitators" to being critical thinkers, problem solvers, and theorem provers.

Exams:

Midterm: Take-home 30 October to 3 November 2017. [Practice Midterm].
Final: 8am-10am on Tuesday 12 December 2017 in Taft Hall 308.

Syllabus:

Axioms for the Integers (AI): [pdf].
Number Theory I (NTI): [pdf].
Induction (I): [pdf].

Homework:

Due Tuesday 9/5 at 5pm on Crowdmark: Proposition AI.6.
Due Tuesday 9/12 at 5pm: Propositions AI.4 and AI.7.
Due Thursday 9/21 at 5pm: Propositions AI.10 and AI.13.
Due Thursday 9/28 at 5pm: Propositions NTI.4 and NTI.7.
Due Tuesday 10/10 at 5pm: Propositions NTI.12, NTI.18, and NTI.21.
Due Thursday 11/2 at 5pm: Propositions NTI.34, NTI.35, and NTI.36.
Due Tuesday 11/21 at 5pm: Proposition NTI.39 and Problems NTI.44 and NTI.46.
Due Thursday 12/7 at 5pm: Theorem I.7, Problem I.11, and Theorem I.16.

Evaluation:

Attendance and Participation 35%, Assignments and Presentations 35%, Exams 30%.
To pass this course with a C, you must demonstrate that you can effectively produce a proof. Your final grade in Math 215 will be determined by the number of points you earn on the following scale: A: 85 -- 100 points, B: 75 -- 84 points, C: 65 -- 74 points, D: 55 -- 64 points, and F: 0 -- 54 points. There will be no curve for the final grade.
You are expected to attend all of the class meetings and to participate actively.
Homework to be done outside of class will require a good deal of writing.
No late homework will be accepted, and you must be present to submit your homework.
Missing five or more classes will drop your final grade by one letter grade. Missing four or more assignments will drop your letter grade by one letter grade. There are no exceptions.
It is your responsibility to be at the exam as no make-ups will be given except under extreme circumstances.
Permission for a non-emergency class absence must be requested at the begining of the term.
You are highly encouraged to work collectively on the homework. You may also look to other sources for solutions. However, you must cite any outside source you have used in finding your solution. And, you must write up your solution in your own words.
I suggest you make a serious attempt at each problem before consulting a peer or another text.
In this course, we will be using LaTeX and Crowdmark to submit all homework. LaTeX is a language used in mathematics (and other disciplines) used to display beautiful formulas. Any mathematics textbook you have read uses some form of LaTeX. To get started using LaTeX, use the following document for instructions on installing it on your machine: directions for installing LaTeX. Once you have installed LaTeX and a GUI, use this document as a starting point for typesetting your homework. You will notice that this template is EXTREMELY boring, and you are encouraged to play around with it and customize it! If you ever want to know if LaTeX can do something (which it usually can), you can always perform a Google search for it by adding "LaTeX" at the end of your search. You can also come see me if you have questions. The website ShareLaTeX provides a way to edit and compile LaTeX files online without installing anything on your computer.

Resources:

The time in class.
The Math Learning Center, in SEO 430.
My office hours, listed above.

Miscellanea:

If you wish to request an accommodation due to a disability, please contact the Disability Resource Center at +1-312-413-2183.
Come to office hours!