SKKU Linear Algebra Syllabus (선형대수학 수업계획서)

(Spring, 2017) 학년도/학기 : 2017학년도 1 학기

(Course Number) 학수번호-분반 : GEDB003-41/42

(General BSM course) 이수구분 : 교양                                

(Course Title) 교 과 목 명 :  Introductory Linear Algebra  (선형대수학)                                                     

◯ (Prof. Sang-Gu LEE) 교강사명, 이상구    


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

◯ (Prerequisite) 선이수과목: 미적분학1 (recommend to have better than C grade from Calculus1)

◯ (Class HR) 수업시간 : 41: Tue[AA] 9-10:15, Thr[BB] 10:30-11:45  (42: 화[BB], 월[AA] )

◯ (Lecture Hall) 강의실 : 자연과학캠퍼스 [32255] 제 2과학관 32동 2층 송천강의실

◯ (Office Hour) 면담시간 : 화요일 시작시간 12:30 ~ 종료시간 14:00                               

◯ (Expected study hours) 자기학습시간 : 예습: 2 시간, 복습 및 PBL 정리: 2시간


◯ (Textbook) 관련 도서 및 참고자료

   (Main Text) Linear Algebra, Sang-Gu Lee et al, 2016, Kyobo Books, BigBook -무료전자책  -전자책 (무료 다운로드)   


          -전자책 (무료 다운로드)  


   (부교재) 현대선형대수학 with Sage, 이상구, 김덕선, 이재화, 2012, 경문사

   (Reference) Contemporary Linear Algebra, Anton and Busby, 2002, Wiley

◯ (Instructional characteristic) 수업 특성 : Flipped/PBL Action Learning Class

GEDB003-41 (Mon 9:00, THR 10:30, International Student, Problem Based Learning)

GEDB003-42 (Mon 10:30, THR 9:00, 학생중심수업, Discussion, Project Based Learning)


◯ (What will be covered and How) 강좌진행 방법 : Selected SKKU Flipped/PBL Action Learning Class: Linear algebra is a branch of mathematics concerned with the study of vectors, vector spaces (also called linear spaces), linear maps (also called linear transformations), and  systems of linear equations.

  Vector spaces are a central theme in modern mathematics; thus, linear algebra is widely used in both abstract algebra and functional analysis.

  Linear algebra also has a concrete representation in analytic geometry and it is generalized in operator theory. It has extensive applications in the natural sciences and the social sciences, since nonlinear models can often be approximated by linear ones. Knowledge of linear algebra is also a central part of numerical and computational mathematics. One of the applications of linear algebra is the solution of simultaneous linear equations. Our Linear algebra course will cover matrix operations, systems of linear equations, vector spaces, subspaces, bases and linear independence, eigenvalues and eigenvectors, diagonalization of matrices, linear transformations, determinants, General Vector spaces and JCF etc.      

  You will have online lectures before the class, and you will make questions and answers in QnA, and we will discuss them in our class. Grade will be based on your performance on the Exam and PBL participation. English will be our official language. We will cover: Vectors, geometric, norm, vector addition, dot product, equality, application of angle between vectors as measure of genetic distance Systems of linear equations and Gauss-Jordan elimination; application to social problems, Matrices, inverses, diagonal, triangular, symmetric, trace, and applications. Determinants, evaluation by row operations and Laplace expansion, properties, eigenvalues and eigenvectors, Differential equations, system of first order linear equations, applications to population dynamics, linear second order differential equations.

You may refer :

◯ (Goal) 교과목 목표 : We will discuss many interesting problems from textbook and Web in English. All should understand most of LA concepts and do small/large size computations of the above concepts and should be able to explain what you found.




◯ (Weekly Contents) 수업내용                                                                  

 Week 1주차   First class : Inner product, Orientation 1.1, 1.2                 

        2주차   Vector (벡 터): 1.3, 2.1, 2.2                                    

        3주차    LSE : *2.3, 3.1  Matrix : 3.2, 3.3                              

 Week 4주차   Matrix 3.4, 3.5, 3.6, *3.7  and Quiz 1 and 1st PBL Report      

        5주차   Quiz 1,  Determinant : 4.1, 4.2, 4.3                            

        6주차   Determinant *4.4, 4.5 Linear Transformations: 6.1 ,6.2         

        7주차   LT  6.3, 6.4, * 6.5, CAS system                                 

 Week 8주차    Chapter 1-6 <Mid term Exam> and Updated PBL/Proposal                    

 Week 9주차   * Matrix Model :  Chapter 5 Sketch

                Dimension and Subspaces : 7.1, 7.2                            

        10주차 Dimension and Subspaces 7.3, 7.4, 7.5, *7.6                   

        11주차 Dimension and Subspaces 7.7, *7.8, 7.9, Review               

        12주차 Diagonalization : 8.1, 8.2, 8.3          

        13주차 Orthogonal matrices, orthogonal similarity. 8.4, *8.5, *8.6, 8.7, 8.8        

        14주차 orthogonal diagonalision *8.9, Chapter 8 Review, 2nd PBL Report

 Week 15주차  General Vector Spaces : 9.1, 9.2*9.3, JCF 10.1                        

        16주차 Ch 7-8-9 Project Presentation and Final Exam                  


Homework 과제물      10-15 Problems in each Chapter of the Textbook      


◯ (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%.                                                                                         

◯ (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.

* 장애학생지원센터: 02-760-1092,


* English Lecture Note (영어 강의록) :                                             

* Korean Lecture Note (한국어 강의록) :

     모바일 CAS 도구 


◯ (Links) 강좌관련 링크

   Related lectures (simulations) :

   Cyber Lab (사이버 실습실) :               

◯ Movie Lectures/Problem solving:  (Flipped/PBL Learning)

LA - first Class - Introduction, (1/2) 

Chapter 1.

LA Sec 1.1, 1.2,  first Class (2/2)

LA Sec 1.3, Vector Equations of Lines and Planes, 

Chapter 2.

LA Sec 2.1, 2.2, Linear System of Equations,

Chapter 3.

LA Sec 3.1, 3.2, 3.3, Matrix Algebra, Part 1,

LA Sec 3.4, 3.5, 3.6, Subspace, Solution Space,

LA Sec 3.7, Special Matrices,

Chapter 4.

LA Sec 4.1, Determinant,

LA Sec 4.2, 4.3. 4.4, Cofactor Expansion,

LA Sec 4.5, Eigenvalues and eigenvectors

Chapter 6.

LA Sec 6.1, Linear Transformation,

LA Sec 6.2, Geometric Meaning of Linear Transformation,


LA Sec 6.3, Kernel and Range

LA Sec 6.4, Composite of LT

  *Problem Solving (Ch 1.-Ch.10)

  LA Problem solving Ch. 1,

  LA Problem solving Ch. 2,

  LA Problem solving Ch. 3,

  LA Problem solving Ch. 4,

  LA Problem solving Ch. 6,

              LA Midterm Review  

  LA Problem solving Ch. 7,   

  LA Problem solving Ch. 8,  

  LA Problem solving Ch. 9,

  LA Problem solving Ch. 10,  

Sample Exam :

Sample Exam :

* Chapter 5. Matrix Model

  5-1 Power Method: 

  5-2 Cryptography: 

  5-3 Blackout Game: 

  5-4 Markov Chains: 

  5-5 Google Matrix: 

  5-6 Project: 

           Ch 5 Matrix Model Project 학생 발표 

LA Midterm Review

Chapter 7. Dimension and Subspaces

LA Sec 7.1, Properties of bases and dimensions,

LA Sec 7.2 Basic spaces of matrix

LA Sec 7.3 Rank-Nullity theorem

LA Sec 7.4 and 7.5  Rank theorem and Projection theorem 


LA Sec *7.6 Least square solution (

LA Sec 7.7 Gram-Schmidt orthonomalization process,


LA Sec 7.8 QR-Decomposition; Householder transformations


LA Sec 7.9 Coordinate vectors

  Section 7-1

  Section 7-5

  Section 7-7

  Section 7-9

Chapter 8. Diagonalization

LA Sec 8.1 Matrix Representation of LT and 8.2 Similarity and Diagonalization,


LA Sec 8.3 Diagonalization with orthogonal matrix, *Function of matrix,


LA Sec 8.4 Quadratic forms,

LA Sec *8.5 Applications of Quadratic forms (

LA Sec 8.6 SVD and  Generalized Inverse,

LA Sec 8.7 Complex eigenvalues and eigenvectors,

LA Sec 8.8 Hermitian, Unitary, Normal Matrices,

LA Sec *8.9 Linear system of differential equations


  Section 8-1  

  Section 8-2


  Section 8-3

  Section 8-4

  Section 8-5

  Section 8-6

  Section 8-7

  Section 8-8


  Section 8-9

Chapter 9. General Vector Spaces

LA Sec 9.1 Axioms of Vector Space,

LA Sec 9.2 Inner product spaces; *Fourier Series,

9.3 Isomorphism,

  Section 9-1

  Section 9-2

  Chapter 9


Chapter 10. Jordan Canonical Form

10.1 Finding the Jordan Canonical Form with a Dot Diagram


*10.2 Jordan Canonical Form and Generalized Eigenvectors,  (

 10.3 Jordan Canonical Form and CAS,    



  Section 10-1

  Chapter 10

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

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

◯ Solution Book for Linear Algebra     

Project Presentation

◯ Sample Final Exam



Reference video:,  

◯ References

1. Math History (수학사)


<사회수학 : 400년의 파란만장 강의>

2. Intro. to Highschool Calculus 

3. Calculus (미적분학, 대학수학)

Part I   Single Variable Calculus

Part II  Multivariate Calculus

미적분학 Lab: 

* '컴퓨팅 사고력(Computational thinking)' 향상과 Sage 도구를 이용한 수학

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

2014 Final Exam of  Calculus(pdf)  

4. Intro. Linear Algebra

(영어 LA 교과서 : 무료 전자 책)

(한국어 LA 교과서 : 무료 전자 책) 


5. 공학수학 Engineering Mathematics with Sage:

[저자] 이상구, 김영록, 박준현, 김응기, 이재화

 (무료 전자책)    (Sample Book1)

       (Sample Book2)



A. 공학수학 1 – 선형대수, 상미분방정식+ Lab

Chapter 00 서문

Chapter 01 벡터와 선형대수

Chapter 02 미분방정식의 이해

Chapter 03 1계 상미분방정식   

Chapter 04 2계 상미분방정식

Chapter 05 고계 상미분방정식

Chapter 06 연립미분방정식, 비선형미분방정식

Chapter 07 상미분방정식의 급수해법, 특수함수 

Chapter 08 라플라스 변환

B. 공학수학 2 - 벡터미적분, 복소해석 + Lab

Chapter 09 벡터미분, 기울기, 발산, 회전

Chapter 10 벡터적분, 적분정리

Chapter 11 푸리에 급수, 적분 및 변환

Chapter 12 편미분방정식

Chapter 13 복소수와 복소함수, 복소미분

Chapter 14 복소적분

Chapter 15 급수, 유수

Chapter 16 등각사상



6. 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:    Communications of Mathematical Education 제 29집 제 4호, 2015. 11. 490-505


7. Linear Algebra and  Matrix Theory: 


<MT-Linear Algebra-All Solutions>

 MT-Chapter 9 Solutions

 MT-Chapter 8 Solutions

 MT-Chapter 7 Solutions:

 MT-Chapter 6 Solutions:

 MT-Chapter 5 Solutions:

 MT-Chapter 4 Solutions:

 MT-Chapter 3 Solutions:

 MT-Chapter 2 Solutions:

 MT-Chapter 1 Solutions: 


8. Linear Algebra and  Matrix Analysis : 


9. Linear Algebra and  Numerical Linear Algebra :


10  Linear Algebra and Math. Modeling : 


11. Mathematics for BigData                                


Professor LEE’s class survey for the first day of this semester :



  Hope you can enjoy this semester with the abobe contents and free math e-book