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SKKU Math Modeling Syllabus

(수학적 모델링 수업계획서)

(Spring, 2017)  학년도/학기 : 2017학년도 1 학기 https://translate.google.co.kr/?hl=ko

(Course Number) 학수번호-분반 : MTH5110-41

(Course Title) 교 과 목 명 : Math Modeling  <Math Modeling and Big Data>

◯ (Prof. Sang-Gu LEE) 교강사명, 이상구 http://matrix.skku.ac.kr/sglee/vita/LeeSG.htm

◯ (Who will take) 수강대상학과 : Open to all Major  + 자연과학부

◯ (Prerequisite) 선이수과목(권장) : Linear Algebra and/or Matrix Theory

◯ (Class HR) 수업시간 : Monday [CC+DD] 12:00-14:45

◯ (Lecture Hall) 강의실 : [32356A] 자과캠 제2과학관 32동 3층 수학과 세미나실

◯ Office Hour : Tueday 12:30 ~ 14:00 + appointment 290-7025, sglee@skku.edu

◯ (Expected study hours)  자기학습시간 : 예습: 3 시간, 복습: 3시간

◯ (Textbook/References) 관련 도서 및 참고자료

Lecture Notes +

Mining of Massive Datasets, Anand Rajara, Jeffrey David Ullman, 2011,

Cambridge Univ. Press

Mathematical Modeling with Excel, Neuwirth and Arganbright, 2004,

Thompson Brooks/Cole

Matrix Analysis, Roger A. Horn, Charles R. Johnson, 1990, Cambridge

Univ. Press

Calculus with Sage, Sang-Gu Lee et al., 2014, KyungMoonSa,

◯ (Instructional characteristic) 수업 특성 : Flipped PBL Class

◯ (What will be covered and How) 강좌진행 방법 : Flipped PBL Class!!

<Math Modeling and Big Data>

Related Course web page : https://canvas.harvard.edu/courses/4766

Big Data refers to both quantity and complexity of the data being produced. To keep up with big data, it is not enough to rely on faster computers with more storage. We need to be smarter. This class discusses the various forms of data which exist and the mathematics used to describe them. It then discusses three important aspects of working with data: data acquisition, data analysis and data visualization, and the mathematics involved in each.

◯ (Goal) 교과목 목표 : This course is designed to teach the mathematical techniques used to acquire, analyze and visualize big data. It focuses on data used in a scientific setting as opposed to a business setting. Mathematical background and some Math Modeling technique will be covered first. Students will be asked to deal with real world problems that each can analyze. Students will then implement their solution using math tools such as SageMath, R and/or Matlab. On the theoretical side, students will be exposed to the challenges posed by big data. The following questions along with the mathematical techniques to answer them will be investigated: how do we represent big data, what are the challenges in acquiring, analyzing and visualizing big data?

◯ (Weekly Contents) 수업내용

Week 1주차  Introduction: Math Moseling and Big Data

2주차  Calculus, Lineal Algebra

3주차  Diff. Equation and Statistics with Tools

Week 4주차  Matrix Analysis 1

5주차  Matrix Analysis 2

6주차  Math Modeling

Week 7주차  Project Proposal (1st PBL report) http://youtu.be/jp3512p-GAs

Week 8주차  Midterm Exam

Week 9주차  [Big Data 1] How Can Mathematics Help

Types of Data, Mathematics to the Rescue!

Week 10주차 [Big Data 2]  Acquisition of Data

Information Content,  Compressed Sensing

Week 11주차 [Big Data 3] Data Analysis

High Dimensional Data, Imaging Data

Week 12주차 [Big Data 4] Tasks :

Removing Noise. Pattern recognition. Reconstructing missing data.

Week 13주차 [Big Data 5]

1 The Mathematical Shape of Things to Come from Quanta Magazine.

2 The Real Secret to Unlocking Big Data? Math.

3 The New Shape of Big Data.

4 New Mathematical Method May Help Tame Big Data from Communications

of the ACM.

5 Better Way to Make Sense of Big Data from Science Daily."

Week 14주차  [Big Data 6] Tools :

Statistics. Fourier and harmonic analysis. Partial differential equations.

Compressed sensing. Linear Algebra.

15주차  [Machine Learning 1]

Week 16주차  Final PBL and Project Presentation

1. Intro. to Highschool Calculus

2. Calculus (미적분학, 대학수학)

http://matrix.skku.ac.kr/Cal-Book/

Part I   Single Variable Calculus http://matrix.skku.ac.kr/Cal-Book/part1/part1.html

Part II  Multivariate Calculus http://matrix.skku.ac.kr/Cal-Book/part2/part2.html * '컴퓨팅 사고력(Computational thinking)' 향상과 Sage 도구를 이용한 수학

http://scholar.ndsl.kr/schDetail.do?cn=JAKO201506960267810

<수학 (미적분학 +선형대수학+미분방정식+복소함수론+공학수학+통계) + (클릭 한번으로) 파이썬 언어 Sage 코딩 교육 + 시각화 + 동시에 무료 계산>

2014 Final Exam of  Calculus(pdf) http://matrix.skku.ac.kr/Cal-Book/2014-Calculus-S-Final-Exam-Final.pdf

3. Intro. Linear Algebra

(영어 LA 교과서 : 무료 전자 책)

http://matrix.skku.ac.kr/LA/

(한국어 LA 교과서 : 무료 전자 책)

4. Engineering Mathematics with Sage:

[저자] 이상구, 김영록, 박준현, 김응기, 이재화

(무료 전자책) http://www.hanbit.co.kr/preview/4210/sample.pdf    (Sample Book1)

http://www.hanbit.co.kr/preview/4209/sample.pdf   (Sample Book2)

Contents

A. 공학수학 1 – 선형대수, 상미분방정식+ Lab

Chapter 00 서문  http://matrix.skku.ac.kr/EM-Sage/Preface.html

Chapter 01 벡터와 선형대수 http://matrix.skku.ac.kr/EM-Sage/E-Math-Chapter-1.html

Chapter 02 미분방정식의 이해 http://matrix.skku.ac.kr/EM-Sage/E-Math-Chapter-2.html

Chapter 03 1계 상미분방정식 http://matrix.skku.ac.kr/EM-Sage/E-Math-Chapter-3.html

Chapter 04 2계 상미분방정식 http://matrix.skku.ac.kr/EM-Sage/E-Math-Chapter-4.html

Chapter 05 고계 상미분방정식 http://matrix.skku.ac.kr/EM-Sage/E-Math-Chapter-5.html

Chapter 06 연립미분방정식, 비선형미분방정식 http://matrix.skku.ac.kr/EM-Sage/E-Math-Chapter-6.html

Chapter 07 상미분방정식의 급수해법, 특수함수 http://matrix.skku.ac.kr/EM-Sage/E-Math-Chapter-7.html

Chapter 08 라플라스 변환 http://matrix.skku.ac.kr/EM-Sage/E-Math-Chapter-8.html

B. 공학수학 2 - 벡터미적분, 복소해석 + Lab

Chapter 09 벡터미분, 기울기, 발산, 회전 http://matrix.skku.ac.kr/EM-Sage/E-Math-Chapter-9.html

Chapter 10 벡터적분, 적분정리 http://matrix.skku.ac.kr/EM-Sage/E-Math-Chapter-10.html

Chapter 11 푸리에 급수, 적분 및 변환 http://matrix.skku.ac.kr/EM-Sage/E-Math-Chapter-11.html

Chapter 12 편미분방정식 http://matrix.skku.ac.kr/EM-Sage/E-Math-Chapter-12.html

Chapter 13 복소수와 복소함수, 복소미분 http://matrix.skku.ac.kr/EM-Sage/E-Math-Chapter-13.html

Chapter 14 복소적분 http://matrix.skku.ac.kr/EM-Sage/E-Math-Chapter-14.html

Chapter 15 급수, 유수 http://matrix.skku.ac.kr/EM-Sage/E-Math-Chapter-15.html

Chapter 16 등각사상 http://matrix.skku.ac.kr/EM-Sage/E-Math-Chapter-16.html

5. Statistics (통계학)

* 무료 전자 도서:  최용석, [빅북총서008] R과 함께하는 통계학의 이해, BigBook, 2014.

[논문] ‘R을 활용한 ‘대화형 통계학 입문 실습실’ 개발과 활용',

'Interactive Statistics Laboratory  using R and Sage',

J. Korea Soc. Math. Ed. Ser. E: Communications of Mathematical Education, Vol. 29, No. 4, Nov. 2015. 573-588.

R을 활용한 ‘대화형 통계학 입문 실습실’ 개발과 활용 韓國數學敎育學會誌 시리즈 E <數學敎育 論文集>  J. Korea Soc. Math. Ed. Ser. E:http://dx.doi.org/10.7468/jksmee.2015.29.4.000    Communications of Mathematical Education 제 29집 제 4호, 2015. 11. 490-505

6. Linear Algebra and  Matrix Theory:

7. Linear Algebra and  Matrix Analysis :

8. Linear Algebra and  Numerical Linear Algebra :

http://matrix.skku.ac.kr/nla/

9  Linear Algebra and Math. Modeling :

10. Mathematics for BigData

http://www.kocw.net/home/search/kemView.do?kemId=1090790   (Midterm Exam)

◯ Lectures Link : Mathematics for Big Data

Lesson 1 Introduction https://youtu.be/EURJnLppzKc

Math for Big Data, Lecture 1, Introduction, https://youtu.be/EURJnLppzKc

Math for Big Data, Lecture 2, LU Decomposition, https://youtu.be/bzhTnoN3atk

Math for Big Data, Lecture 3, Schur Decomposition

https://youtu.be/F2kZON0oS_w

Math for Big Data, Lecture 4, Power Method,  https://youtu.be/n4KD4aq_jxw

Math for Big Data, Lecture 5, QR Decomposition, https://youtu.be/gQ7gxTx5f9k

Math for Big Data, Lecture 6, Google's PageRank algorithm

https://youtu.be/tp6B7s43jAI

Math for Big Data, Lecture 7, Singular Value Decomposition(SVD)

Math for Big Data, Lecture 8, Least Square Solutions

Math for Big Data, Lecture 9, Polar Decomposition, NMF

Math for Big Data, Lecture 10, Finding JCF using Dot Diagram,

Math for Big Data, Lecture 11, Generalized eigenvectors and Matrix Function,

https://youtu.be/lK4_Kp6P_N4

Math for Big Data, Lecture 12, Principal Componant Analysis 1 (PCA)

Math for Big Data, Lecture 13, Principal Componant Analysis 2 (PCA)

https://youtu.be/j8PAt_Al180

Math for Big Data, Review 1, Intro. Calculus, Team 4

https://youtu.be/qALN6OAwNUo

Math for Big Data, Review 2, Intro. Linear Algebra, Team 3

https://youtu.be/xrFqBe8Rhs4

Math for Big Data, Review 3, Intro. Statistics, Team 2, https://youtu.be/sOx74EntB0I

Math for Big Data, Review 4, Intro. Engineering Math, Team 1

Math for Big Data, Midterm PBL, S. Sun, https://youtu.be/CSdciSMPm-8

Math for Big Data, Midterm PBL, Naguib, https://youtu.be/k9_Ie8bMAY0

Math for Big Data, Midterm PBL,  KEAhn, https://youtu.be/xFJmI1_uynk

Math for Big Data, Midterm PBL, Choo, https://youtu.be/TlC78z_LErQ

Math for Big Data, Midterm PBL,  Naeem, https://youtu.be/8xo5UOP1tu8

Math for Big Data, Midterm PBL,  Lkhagva, https://youtu.be/pPtO1rNdLs0

Math for Big Data, Midterm PBL,  Sudip, https://youtu.be/5md49_RG74Q

Math for Big Data, Midterm PBL, Jeongwon Pyo, https://youtu.be/u5zDWtmx9P0

Math for Big Data, Midterm PBL,  ESJang, https://youtu.be/cHYvWBuBrFA

Math for Big Data, Lecture 14,  Graph and Matrix, https://youtu.be/Z89XvKXIYeg

Math for Big Data, Lecture 15,  Laplacian Matrix and Big Data

Math for Big Data, Lecture 16, Intro. Big Data for Machine Learning 1

https://youtu.be/P24A1fkpX-Y

Math for Big Data, Lecture 17,  Intro. Big Data for Machine Learning 2

Math for Big Data, Lecture 18,  (Team 4) Intro. Data Mining, Ahn& Choo

Math for Big Data, Lecture 19,  (Team 1) Pattern Classification 1, Naguib & Naeem

Math for Big Data, Lecture 20,  (Team 1) Pattern Classification 2, Naguib & Naeem

Math for Big Data, Lecture 21,  (Team 2) Statistical Learning

Math for Big Data, Lecture 22,  (Team 3) Cluster Analysis

Math for Big Data, Lecture 23,  (Team 3) Project Draft 1

Math for Big Data, Lecture 24,  (Team 3) Project Presentation, Spectral Cluster Analysis by Shaowei-Lkhagva, https://youtu.be/476HgeBM8AE

Math for Big Data, Lecture 25,  (AV) Project Presentation, Restricted Boltzmann Machine Training of Perceptron for Clustering by Naguib-Naeem

Math for Big Data, Lecture 25,  (Team 1) Project Presentation, Restricted Boltzmann Machine Training of Perceptron for Clustering by Naguib-Naeem

Math for Big Data, Lecture 26,  (Team 2) Project Presentation,Hand Gesture Recognition with Convolutional Neural Network by Pyo-Sudip-Jang

Math for Big Data, Lecture 27,  (Team 4)

Math for Big Data, Lecture 28,  Final PBL Presentation by Sudip,

https://youtu.be/cOwWZcVb1AU

(Final Exam)

○ (Project & PBL) 과제물 :

Reading the sections of the text related to the problems is part of the homework assignment. Assigned problems will be posted after each class.  You will create  some Mathematical Model in your working area. Schedule of Activities: Homework and reading assignments will be given on a weekly basis.

◯ (Evaluation) 평가 :

출석/발표 20%, 과제/토론 20%, 중간시험 20%, 기말시험 30%, 기타 10%

Participation/Presentation 20%, HW-Quiz-PBL report-etc-30%, Exams 20+30=50%.

Grading: The final grade will be the average of all the assigned projects. PBL report will be collected and it will be discussed in class. Grading will be based on projects related to the material studied, given throughout the semester and a final project. All students will present their final project in class.

◯ (Honor Code) 유의사항 : ※ 시험 부정행위, 기타 부정한 방법으로 취득한 과목의 성적은 F 처리됩니다.  (성균관대학교학칙 시행세칙(학사과정) 제25조, 시행세칙(대학원과정) 제31조)

◯ (Handicapped students) 장애학생 지원안내

장애학생은 본 수업과 관련하여 본인 희망 시 수업도우미 및 학습지원을 위한 조정(강의자료 사전 제공, 과제 및 평가 조정, 과제 제출기한 연장, 시험시간 연장 등)이 가능하오니, 필요한 학생은 수강신청 전 교수님 및 장애학생지원센터에 상담하여 주시기 바랍니다.

* Help desk 장애학생지원센터: 02-760-1092, supporter@skku.edu