215 - Introduction to advanced mathematics - Fall 2015 - UIC

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Time: 10:00-10:50am MWF.
Place: Addams Hall (AH) 306.

E-mail: benjamin.antieau@gmail.edu.
Course webpage: dantie1.people.uic.edu/201503-215.html.

Office hours: 11:00am-12:00pm Mondays and 12:00-1:00pm Wednesdays in SEO 419.

Book: there is no book required for this course.

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.

Syllabus:

Number Theory I: [pdf].
The Real Numbers: [pdf].
Sets: [pdf].
Induction: [pdf].
Number Theory II: [pdf].
Midterm: Friday 9 October, in class.
Final: Friday 11 December, 10:30am-12:30pm. [Practice final].

Homework:

Due Wednesday 8/26: NTI.3 and NTI.4.
Due Monday 8/31: NTI.7, NTI.11, and NTI.12.
Due Friday 9/4: NTI.2.5 and NTI.2.8.
Due Friday 9/11: RN.6, RN.9, and RN.14.
Due Friday 9/18: S.13, S.17, and the last bullet from S.18.
Due Wednesday 9/23: S.27 and S.29.
Due Friday 10/2: NTI.33, NTI.34, ~~and NTI.35~~.
Due Wednesday 10/21: I.1 and I.4.
Due Monday 10/26: I.6 and I.7.
Due Monday 11/2: I.11 and I.12.
Due Friday 11/13: NTII.3 and NTII.7.

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 in advance.
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.

Resources:

The time in class.
The Math Learning Center, in SEO 430.
My office hours, listed above.
The optional textbook, Eccles, An introduction to mathematical reasoning.
piazza.com.

Miscellanea:

We will use piazza.com for discussion outside of the course.
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!