Math103/GEAI1215 Linear Algebra I | 線性代數（一）

Announcements

Course Info top

Textbook

線性代數筆記本
   Jephian Lin

Linear Algebra [ pdf answers ]
   Jim HefferonCourse website

Further Resources

Essence of linear algebra
   3Blue1Brown

LA Tea: 利用喝杯茶的時間，來聊點線性代數吧！

Learning objectives

The notion of points, lines, and planes can be generalized into affine subspaces in a higher-dimensional space. This course will revisit some vector/matrix algebra, learn the definition of an affine subspace, and use it to describe the solution set of a system of linear equations. Moreover, we will learn how to build a coordinate system (basis) on an affine subspace and determine its dimension. Lastly, we will introduce the linear functions and how to use matrices to represent them.

Outlines

Evaluation

15% Group Homework + 10% Active Learning + 3*5% Quizzes + 3*20% Exams

Tentative Schedule top

Calendar

Homework/Quiz top

There are 3 group homework assignments and 3 quizzes.

Group Homework: Each section in LA notebook contains several exercises. You will be assigned with three sections, and you and your group have to finish the exercises. Collaboratively, by the end of the semester, we will build a customized linear algebra notebook just for us. This can be helpful when you are preparing linear algebra exams in the future (such as for graduate school applications). See NSYS Cyber University > 課程公告板 more details.

Active Learning: It is critical that you cultivate your active learning skills, which are not just for this course. You have to learn how to make a learning plan for yourself and how to stick with your plan. In this course, we introduce two things that you can do on a daily basis: one is for English learning, and the other is for mathematics learning.

  1. VoiceTube 口說挑戰: Listen to the sentence and record your voice. That's it! You will learn new vocabularies day by day and build your listening/speaking skills at the same time.
  2. Play with a mathematics concept: Memorizing something is the very basic level of understanding. To understand a concept, you have to keep playing with it in your brain. For example, we will learn very soon that for any system of linear equations, the number of solutions is either \(0\), \(1\), or \(\infty\) (so it cannot be any finite number other than \(0\) or \(1\)). Once you have learned this idea, you may ask yourself lots of questions:
    • Is there an example with no solution? Is there an example with one solution? How about an example with infinitely many solutions?
    • If I see a system of linear equation, how do I determine the number of solutions? Why these criteria work?
    • What is the difference between a linear equation and a polynomial equation? (Obviously, \(x^2 - 3x + 2 = 0\) has two solutions.)
    Try to throw a question to yourself every once in a while, and try to catch it by answering the question. You will gain deeper understand of the concept. And more importantly, it's fun!

See NSYS Cyber University > 課程公告板 for more details.

Quizzes: The question type of each quiz will be given but the numbers will be different. No partial credits for quizzes. However, within the two weeks (and before the final exam) after a quiz is given, you may ask for extra tests of the same question type. Your score for a quiz is the average of all tests you have taken under the same question type. Note: If you missed the quiz in class, that counts as a zero.

For example, you missed Quiz 1 in class, and you asked for 3 extra tests and get 2 of them correct, then your score for Quiz 1 is (0 + 5 + 5 + 0) / 4 = 2.5.

Exams: After each exam, the questions and the sample answers will be uploaded below.

Policies/Ethics top

Accessibility

Students with diverse learning styles and needs are welcome in this course. In particular, if you have a disability/health consideration that may require accommodations, please feel free to approach me.

Grading

Percentage scores will be converted to letter grades according to the university-wide standard table.

Attendance

You are expected to attend the classes.

Missing work

If you miss some course components due to illness, accident, family affliction, or religious observances, please talk to me and provide the documentation. In such cases, the course component is excused, and your course score will be calculated by distributing the weight of the missed item(s) across the other course components. Missing components are limited to at most 20%.

Academic integrity

Do not copy others' work, including others' homework, the textbook, online materials, and others' answers in an exam; if it is really necessary, add proper citations to your references. It makes no point (and gives you no point) if the work is not yours since you learned nothing.