**Fundamental Mathematics**

_______________________________________

**Instructor:** Prof. Zhong-Jin Ruan

**Classroom/Time: ** Section B1: 143 Henry Bld, MWF 9:00 - 9:50am

** ** Section D2: 141 Altgeld Hall MWF 11:00-11:50am

** Office Hour:** MW 10:00-11:00am at 353 AH or by appointment.

** Email:** z-ruan@illinois.edu

**Course Web Page: ** https://faculty.math.illinois.edu/~ruan/347Sp18.html

**Textbook:** Mathematical Thinking: Problem-Solving and Proofs by
D'Angelo and West. 2nd edition.

**Homework:** Homework will be assigned each week and will be
**due in class** on the following days:

** Part I: ** Jan 24, 31, Feb 7 and 14;

** Part II: ** Feb 28, Mar 7, 14 and 28;

** Part III: ** Apr 11, 18, 25 and May 2.

**No late homework will be accepted. ** If you have a reasonable excuse for missing an

assignment, I will score it by taking the average of the other assignments.

**Grading policy:**There will be total of 500 points computed as follows.

Homework | 10 x 10 pts | 100 pts |

Exams | 2 x 100 pts | 200 pts |

Final Exam | 200 pts | |

Total | 500 pts |

Your final grade will be based on the total scores.

**HOMEWORK ASSIGNMENTS **
** ********************************************************* **
** PART I**

******
** HW #1 ** Practice Homework: Page 20, 1.15, 1.20, 1.r1, 1.43, 1.49.

Hand-in Homework: Page 20, 1.13, 1.32, 1.36, 1.44a, b, 1.47a, 1.50 **(Due Wednesday, January 24, 2018)**

** HW #2** Practice Homework: Page 44, 2.4, 2.9, 2.21, 2.25, 2.27.

Hand-in Homework: Page 44, 2.22, 2.23, 2.35, 2.38, 2.47 and the following problem:

Let n be an positive integer. Show that q = \sqrt n + \sqrt 2 is an irrarional number.
** (Due Wednesday, January 31, 2018).**

** HW #3 ** Hand-in Homework: Page 71, 3.7, 3.17, 3.26, 3.49b, 3.56b, 3.57.
** (Due Wednesday, February 7, 2018).**

** HW #4 ** Hand-in Homework: Page 95, 4.20a, b, 4.24, 4.25a, b, e, 4.33a, b, 4.34a, c, 4.46, and 4.47.
** (Due Wednesday, February 14, 2018).**

** Exam1 **
will be given on Monday, February 19,2018 at classroom during class time.
** See solution
[pdf]
**

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** PART II Real Analysis**

******

We would like to recommend the following book and chapters:

1. Textbook: chapter 13 and chapter 14.

2. Introduction to Real Analysis by R. Bartle and D. Sherbert, 4th edition: chapter 2 and chapter 3.

**HW #5**
[pdf],
** Solution **
[pdf],

** Note: There is a minor typo in HW5.3. We should read: ..., but the number u + 1/n is an upper bound of S. (Not: n + 1/n).
**

** HW #6**
[pdf],
** Solution **
[pdf],

** HW #7**
[pdf],
** Solution **
[pdf],

** HW #8**
[pdf],
** Solution **
[pdf],

** Exam2 Review Practice**
[pdf],

** Exam2** will be given on Monday, April 2, 2018 at classroom during class time.

** Exam 2 Solution:** Section B1 Solution
[pdf], Section D2 Solution
[pdf],

** ***************************************
PART III
**************

Additional Problem: Show that 5^{1/3} is an irrationall number.

(1) Find the digraph of the map f_a : Z_{13} -> Z_{13} for \bar{a} = \bar{3}, \bar{4}, and \bar {7}, respectively.

(2) Find the order and the inverse of \bar{3}, \bar{4}, and \bar{7} in Z_{13}.

(1) Find all \bar{b} in Z_{12} such that the congruence equation \bar{8} \bar{x} = \bar{b} has a solution.

(2) Find all solutions for each \bar{b} found in part (1).

I will hold an extra ``Office Hour'' at 141 Altgeld Hall on Thursday (May 3) at 3:00-3:50pm. I will try to return your HW12 during this time, and you can check your scores for this class at that time.

Math347 Section D2 will take Final Exam at classroom 141 Altgeld Hall on May 4 Friday at 1:30-4:30pm.

Math347 Section B1 will take Final Exam at classroom 143 Henry Bldg on May 10 Thursday, at 1:30-4:30pm.

1.Final Exam is a close book exam. So no book, no lecture notes, and no cell phone during the exam.

2. Bring your student ID with you in case we need it.

3. Please come to exam on time. No make up exam unless you have a strong reason, getting my approval before the exam.