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MA1101R Linear Algebra I 2013/2014 Semester I
Lecture Hours (@ LT27): Tue 4.00-‐5.30pm/Fri 4.00-‐5.30pm
IVLE WEBPAGE: https://ivle.nus.edu.sg/ Lecturer: Dr Ng Kah Loon Email: [email protected]; Office: S17, #07-‐20; Tel: 6516-‐2751 Assessment: • Final examination 70% -‐ 29th November (9.00 – 11.00am) (2 helpsheets) • Mid-‐term test 20% -‐ Week 7 during either Tue or Fri Lecture (1 helpsheet) • Lab Quiz 10% -‐ Week 13 Aims and objectives: This module serves as an introduction to the most basic concepts in linear algebra that are routinely applied in fields like science, engineering, statistics, economics and operations research. The vector spaces within which the general ideas are developed are all real vector spaces (actually Rn). The objective of the course is to inculcate a facility in both the algebraic and geometric viewpoints of linear algebra. The course will develop basic skills in computing with vectors and matrices. Main topics: Systems of linear equations. Matrices. Determinants. Euclidean n-‐space. Subspaces. Linear independence. Basis and dimension. Rank of a matrix. Orthogonality and orthonormal bases. Eigenvalues and eigenvectors. Diagonalization and orthogonal diagonalization. Linear transformations from Rn to Rm. Applications. Textbook: • The textbook Linear Algebra-‐Concepts and Techniques on Euclidean Spaces (by Ma S.L.,
V. Tan, Ng K.L. published by McGraw Hill) is available for purchase at Co-‐op (Science).
• The lectures will follow the textbook closely. All 7 chapters in the book will be covered. • Students are expected to work through the exercise sets in the books. There is no need
to hand in the answers of the exercises. Selected problems will be discussed during tutorial sessions.
Tutorial sessions: • There are altogether 11 tutorial sessions, starting from week 3. • Each week, selected exercise problems from the textbook for topics that have been
covered in lectures up to the previous week will be discussed. • Students may be asked by their tutor to present solutions.
Lab sessions: • There will be 5 lab worksheets in total. They will be distributed during weeks 4, 6, 8, 11
and 12. • There will be one lab quiz in week 13. • Students will be using MATLAB to complete their worksheets. • There is no formal class structure for lab. Students are allowed to go to the Computer
lab (S17-‐03-‐02) anytime, during the stated times below: o Wednesday 9am – 11am o Thursday 11am – 2pm o Friday 12 – 4pm
• Once a student completes the lab worksheet for that week, he/she will be allowed to leave the lab. No attendance will be taken. There is no need to submit any completed worksheets.
• During the above time slots, there will be a Lab Assistant stationed in the lab to assist students who may have queries.
• If a student is unable to go to the lab in any of the time slots given above (due to timetable clashes), he/she may go to the lab at a time convenient to them, provided the lab is not being used by another module. However, there will not be any Lab Assistant present during other time slots.
• Availability of computers in the lab is on a first come first served basis. The Lab Assistant will resolve any disputes.
• There WILL be formal class registration for the quiz in Week 13. More details will be available in due course.
Signing up for tutorial groups: • NUS students: Through CORS balloting: 16th – 20th August • NUS students: Manual registration (with lecturer, if failure to obtain a group through
CORS balloting): 21st – 22nd August • Exchange and all other non-‐graduating students: Contact lecturer between 13th to 20th
August. • Contact lecturer as soon as possible for any problem with tutorial group.
Online discussion forum • An online forum has been opened for students to post anything (queries, thoughts,
comments, suggestions …) about this module. • Access through module webpage or IVLE. Consultation booking • Lecturer is available for consultation on an ad-‐hoc basis. Prior appointment (via email)
can be made to see the lecturer for consultation/clarification of concepts. • All students are encouraged to seek help early if they have difficulty with the module
and not wait till the last minute. • Reference Books:
Title/ Authors (Remarks) Publisher
Elementary Linear Algebra / Howard Anton (For understanding basic concepts) Wiley
Linear algebra with applications / Steven Leon (With MATLAB exercises) Prentice Hall
Schaum's outline of theory and problems of linear algebra/ Seymour Lipschutz (Plenty of solved problems) McGraw Hill
Linear Algebra/ Stephen H. Friedberg (Advanced reading) Prentice Hall
Week Lecture Tutorial / Lab Remarks
Week 0 5th Aug – 9th Aug
No Lectures
Orientation Week
Week 1 12th Aug – 16th Aug
Lecture 00 (Introduction)
Lecture 01 (Chapter 1)
Week 2 19th Aug – 23rd Aug
Lecture 02 (Chapter 1)
Lecture 03 (Chapter 1)
Week 3 26th Aug – 30th Aug
Lecture 04 (Chapter 2)
Lecture 05 (Chapter 2)
Tutorial 01
Week 4 2nd Sep – 6th Sep
Lecture 06 (Chapter 2)
Lecture 07 (Chapter 2)
Tutorial 02
Lab 01
Week 5 9th Sep – 13th Sep
Lecture 08 (Chapter 3)
Lecture 09 (Chapter 3)
Tutorial 03
E-‐Learning Week
Week 6 16th Sep – 20th Sep
Lecture 10 (Chapter 3)
Lecture 11 (Chapter 3)
Tutorial 04
Lab 02
Recess Week 21st Sep – 29th Sep
Week 7 30th Sep – 4th Oct
Lecture 12 (Chapter 3)
Mid Term Test
Tutorial 05
Mid-‐ Term Test this week (date to be
advised) Week 8
7th Oct – 11th Oct Lecture 13 (Chapter 3)
Lecture 14 (Chapter 4)
Tutorial 06
Lab 03
Week 9 14th Oct – 18th Oct
No Lecture
Lecture 15 (Chapter 4)
Tutorial 07
15th Oct (Tue) is a Public Holiday
Week 10 21st Oct – 25th Oct
Lecture 16 (Chapter 6)
Lecture 17 (Chapter 6)
Tutorial 08
Week 11 28th Oct – 1st Nov
Lecture 18 (Chapter 5)
Lecture 19 (Chapter 5)
Tutorial 09
Lab 04
Week 12 4th Nov – 8th Nov
Lecture 20 (Chapter 5,6)
Lecture 21 (Chapter 7)
Tutorial 10
Lab 05
Week 13 11th Nov – 15th Nov
Lecture 22 (Chapter 7)
Lecture 23 (Revision)
Tutorial 11
Lab Quiz
Reading Period 16th Nov – 22nd Nov
Examination 29th Nov (Friday AM)
Tutorial Problem Sets
T1: Chapter 1 Exercise 1: Questions 4, 12, 15, 24, 27, 30
T2: Chapter 2 Exercise 2: Questions 3, 8, 10, 17, 21, 23
T3: Chapter 2 Exercise 2: Questions 26, 32, 39, 44, 51, 52
T4: Chapters 2, 3 Exercise 2: Questions 54, 60. Exercise 3: Questions 5, 9, 11, 15
T5: Chapter 3 Exercise 3: Questions 21, 25, 27, 30, 32, 33
T6: Chapter 3 Exercise 3: Questions 34, 36, 37, 39, 40, 42
T7: Chapters 3, 4 Exercise 3: Questions 43, 46, 49 Exercise 4: Questions 2, 3, 5
T8: Chapter 4 Exercise 4: Questions 9, 11, 17, 21, 23, 24
T9: Chapter 6 Exercise 6: Questions 5, 8, 11, 15, 17, 20
T10: Chapter 5 Exercise 5: Questions 7, 10, 14, 17, 19, 21
T11: Chapters 5, 6, 7 Exercise 5: Questions 24, 26, 28 Exercise 6 : Questions 24, 28 Exercise 7 : Questions 2, 3