線性代數筆記本
Jephian Lin
Linear Algebra [ pdf answers ]
Jim HefferonCourse website
Essence of linear algebra
3Blue1Brown
LA Tea: 利用喝杯茶的時間，來聊點線性代數吧！
This course will help you to understand the meaning and the properties of the determinant, which is critical for matrix diagonalization. We will then see many applications of matrix diagonalization: finding a nice coordinate system for a quadratic curve, solving a system of linear differential equations, solving a recurrence relation, and finding the matrix exponential. Theories behind the scene will be provided. Then we will move on to the theory of symmetric matrices, seeing they are always diagonalizable with an orthonormal eigenbasis and real eigenvalues. If time allows, we will go through various advanced topics, such as the principal component analysis, the interlacing theorem, the spectral clustering, and so on.
15% Group Homework + 10% Active Learning + 3*5% Quizzes + 3*20% Exams
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.
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.
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.
Percentage scores will be converted to letter grades according to the university-wide standard table.
You are expected to attend the classes.
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%.
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.