## > Teaching > Adcanced Mathematics C1

### Advanced Mathematics C1

This course and its subsequent Advanced Mathematics C2 cover the most fundamental mathematical tools for business and economics students. Topics contain sets and logics, equations, matrix algebra, functions, derivatives and optimization, and integrals. The purpose of the courses is helping students raise their ability of mathematical thinking in order to better understand other subject.

#### Course Information

**Course ID**: 0208520001

**Credit**: 4

**Lecture time**: Session 9-10 (16:00-17:25) on Monday/Thursday

**Classroom**: South 105, Square Building, Lihu Campus (丽湖校区四方楼南105)

**Instructor**: Jia-Ping Huang

**Office hour**: Please contact the following email address

**E-mail**: huangjp #at# szu . edu . cn

#### Online Learning Platform

We use Tencent Meeting (aka VooV Meeting for out-of-China markets).

Download Tencent Meeting client: https://meeting.tencent.com/download-center.html

Download VooV Meeting client: https://voovmeeting.com/download-center.html

Tencent Meeting is designed as an online meeting platform rather than a learning platform, so although its quality of video and audio is high (which is the main reason of choosing it), other functions such as recording attendance and submiting assignments are insufficient. Therefore we may use other platforms occasionally for such purposes.

**Feb 28, 2022**: Another drawback of Tencent Meeting is that the playbacks cannot be viewed in a convenient way, especially for those who miss the meetings and want to watch the playbacks afterward. Engineers are working on this issue. For now, I will share the link of the playback after each class. You need to follow the instruction on the page the link leads to, and request permission to view the playback.

#### Prerequisites and Suggestions

Knowledge of pre-university mathematics is not required. A graphing calculator may be useful for self-study but is not necessary for the course and is forbidden in exams. Students may also use online tools such as WolframAlpha (https://www.wolframalpha.com/) to deepen their understanding.

#### Textbook

Knut Sydsaeter et al. (2016). *Essential Mathematics for Economic Analysis*, Fifth Edition. Pearson.

#### Topics to be Covered

Chapter 1: Essentials of Logic and Set Theory

Chapter 2: Algebra

Chapter 3: Solving Equations

Chapter 15: Matrix and Vector Algebra

Chapter 16: Determinants and Inverse Matrices

Chapter 4: Functions of One Variable

Chapter 5: Properties of Functions

#### Grading

Attendance: 40%

Final exam: 60%

#### Homework Exercises

- Homework 1 (
**March 7**)- Section 1.1: 1, 4, 6
- Section 1.2: 2(c,e), 4(a)
- Section 1.3: 3
- Section 1.4: 1, 2

- Homework 2 (
**March 17**)- Prove that \( \sqrt{2} \) is an irrational number.

Hint: If \( \sqrt{2} \) is a rational number, we can always find integers \(p\) and \(q\) such that \( \sqrt{2} = p/q \) where \(q\neq 0\), and \(p, q\) are not both even (because if they are, we can cancel the common factor 2 and call the resulting numerator and denominator \(p\) and \(q\) respectively). Assume \( \sqrt{2} \) is rational and then try to find a contradiction. - Section 2.2: 4(b,d,f), 5(c,g,i)
- Section 2.3: 2(a), 3(f), 9(d), 10(a,e)
- Section 2.4: 2(b,e), 5(a,e)
- Section 2.5: 1(e,h), 4(b,e,g), 5(b,c)

- Prove that \( \sqrt{2} \) is an irrational number.
- Homework 3 (
**March 28**)- Section 2.6: 2(b,d), 4(e,”ell”)
- Section 2.7: 2
- Section 2.8: 2(b,c), 3(d,e)
- Section 2.9: 1

- Homework 4 (
**April 7**)- Section 3.1: 1(d), 3(b), 5(c)
- Section 3.3: 2(b,e), 4(e)
- Section 3.4: 1(e,f)
- Section 3.6: 2(a), 3(a)

- Homework 5 (
**April 18**)- Section 15.1: 3
- Section 15.3: 2, 3, 5, 7
- Section 15.4: 1, 2

- Homework 6 (
**April 28**)- Section 15.5: 1, 2(a), 4
- Section 15.6: 1(a,c), 2
- Section 15.7: 7
- Section 15.8: 1, 6

- Homework 7 (
**May 12**)- Section 16.1: 3(a,b), 4, 6
- Section 16.2: 3(c)
- Section 16.3: 1(b), 2, 3

Hint to 16.3.2: first show that \( A B\) is also upper triangular.