MTH028 Linear Algebra I — Syllabus and Teaching Plan (2026–2027 S1)

Author

Jiaye Xu

Published

September 7, 2026

1 Course Information

  • Module: MTH028 Linear Algebra I - Fall 2026
  • Lecture Time & Location:

    • G24: SA136, Monday 4:00 - 5:50 p.m.,

    • G28: SA136, Tuesday 4:00 - 5:50 p.m.,

    • G29: SA136, Wednesday 9:00 - 10:50 a.m.,

    • G34: SB120, Thursday 11:00 a.m. - 12:50 p.m.

  • 课程名称（中文）： 线性代数 I

2 Instructor

  • Dr. Jiaye Xu (徐嘉烨)

  • Email: Jiaye.Xu@xjtlu.edu.cn

  • Website: https://jiayexu.quarto.pub/

  • Office: MB 421B

  • Office Hours: Tuesday, 11:30 - 15:30

3 Textbook

David C. Lay, Steven R. Lay, Judi J. McDonald, Linear Algebra and Its Applications, 6th Edition, Pearson.

We will follow the core chapters: 1–3 (Sections 3.1–3.2) and Chapter 5 (Sections 5.1–5.3).

4 Outline of Lectures

Week Lecture Topics Lecture Notes
W1 L1 1.1 Systems of Linear Equations Chapter 1
W2 L2 1.2 Gaussian Elimination
W3 L3 1.3 Vector Equations; 1.4 Matrix Equation
University Close days (Sep 25 – Oct 4, 2026)
W4 L4 1.5 Homogeneous Systems; 1.7 Linear Independence
W5 L5 1.8 Introduction to Linear Transformations; 1.9 Matrix of a Linear Transformation
W6 L6 2.1 Matrix Operations; 2.2 Inverse of a Matrix (part 1) Chapter 2
W7 L7 2.2 Inverse (cont.); 2.3 Characterizations of Invertible Matrices
W8 L8 2.8 Subspaces of ℝⁿ
W9 L9 2.9 Dimension and Rank
W10 L10 3.1 Introduction to Determinants Chapter 3
W11 L11 3.2 Properties of Determinants
W12 L12 5.1 Eigenvectors and Eigenvalues; 5.2 Characteristic Equation Chapter 5
W13 L13 5.3 Diagonalization; Course Review

Note: All lecture notes are provided via the links above. They are designed to be self‑contained, concise, and aligned with the textbook – but written in more accessible English than the full textbook.

5 Why Linear Algebra?

  • Compulsory course (Pre‑Major, 2.5 credits) – essential for nearly all STEM, business, and data‑science pathways.
  • Foundation for advanced topics – machine learning, optimization, differential equations, quantum mechanics, economics, and more.
  • Rigorous thinking – develops abstract reasoning and problem‑solving skills that are valuable in any quantitative field.

Important: Unlike calculus, linear algebra is a completely new topic – you have not seen it in high school.
This is exactly why many first‑year students find it more challenging than calculus at first.
Do not panic – we will build everything from the ground up, step by step. The course is designed for beginners.

6 Learning Resources

6.1 📘 Textbook

  • Read before class to get an overview; read after class in depth.

6.2 🖥️ Quarto Web Notes (Lecture Notes)

  • Available at the links in the lecture outline above.
  • Advantages over the textbook:
    • Written in plain, straightforward English – easier to follow than the dense textbook.
    • Step‑by‑step explanations with worked examples, not just definitions.
    • Better continuity than PowerPoint slides – you can read them like a book, which helps you connect ideas and build a mental network of concepts.
    • Include visualisations and annotations that clarify abstract ideas.

6.3 📂 Learning Mall Core (LMC)

  • This is our central platform for:

    • Announcements. (Announcements will also be sent to your email address.) Please Check your XJTLU email regularly – all formal announcements (including exam arrangements and deadline changes) will be sent via email.

    • Module Handbook and Teaching Plan – they contain all official policies and schedules.

    • Assignment submission (paper and online)

    • Lecture slides (Web link and PDF version)

    • Supplementary Learning Resources

    • Grade tracking

  • Please check LMC regularly
    👉 Go to Learning Mall Core (you will find the MTH028 course page after login).

6.4 ✏️ Practice & Help

  • Learn by doing – work through the problem sets by yourself every week.
  • Learn by explaining – use the Feynman technique: teach a concept to a friend or to yourself.
  • Group study – discuss problems with classmates.
  • Office hours – come with questions; I am here to help.

7 Assessment

Component Type Weight Timing
Weekly Assignments Written (handwritten) 15% Weekly (W2–W12)
In-Semester Examination Computer‑based (question bank) 20% Weekend of W9
Final Examination Written (paper & pen) 65% After W13
Total 100%

7.1 Weekly Assignments (15%)

  • There will be 11 weekly assignments in total. Your coursework mark will be calculated based on the best 10 out of 11 (so you can drop your lowest score).
  • Submission: All weekly assignments must be submitted via Learning Mall Core (LMC). Submissions sent by email or as hard copies will be ignored. (Late submissions will not be accepted!)
  • Format requirements:
    • Solutions must be handwritten clearly (legible, dark ink).
    • Typed solutions, red‑ink solutions, or illegible work will not be graded.
  • Exercises Booklet: We provide an electronic version of the Exercises Booklet. Part of Chapter 1 is already available on LMC (Public Area), and the complete booklet will be uploaded in September.
  • The scope and deadline for each weekly assignment are clearly stated in the teaching plan and in the submission link on LMC (Please combine all the solutions for each weekly assignment into a single PDF file under 10 MB and make sure that the submitted PDF file can be opened by Adobe Acrobat Reader). The exercise file for each assignment is also attached to the corresponding submission link.

7.2 In‑Semester Examination (20%)

  • Schedule: Based on the latest information, this exam will be held on the weekend of Week 9 in the SIP labs.
  • Seating & Session: Your specific session, seat number, and lab location will be released on e-bridge by Week 2.
  • Format: Closed‑book, invigilated, computer‑based test.
  • Question bank: The system draws from a bank of approximately 15,000 questions. Each student receives a unique paper generated from this bank.
  • Feedback: One generated paper, along with detailed solutions, will be provided to you after the exam for self‑review.

7.3 Final Examination (65%)

  • Format: Written (paper‑and‑pen), closed‑book, invigilated.

  • Question types: The exam consists of four kinds of questions:

    1. True or False
    2. Multiple Choice Questions (MCQ)
    3. Fill‑in‑the‑blank
    4. Comprehensive / Open-ended Questions

  • Schedule: Based on the latest information, the final exam will be held on either the Monday or Tuesday following Week 13. The final timetable will be released by the Registry on e-bridge.

7.4 Online Exercises (Formative Assessment – 0%)

  • These are optional, zero‑weight online exercises offered in Weeks 5, 7, 9, 11, and 13.
  • They serve as mock tests to help you prepare for the In‑Semester Examination.
  • The questions are drawn from the same question bank as the In‑Semester Exam, so you can familiarize yourself with the format and the system.

8 Academic Integrity

This is REALLY important!
Please read the XJTLU Academic Integrity Policy carefully.

Remember:
- ❌ No copying – from any source, including other students, the internet, or AI tools.
- ❌ No collusion – working together is encouraged, but you must write your own solutions in your own words.
- ✅ Cite sources when you use external ideas.
- ✅ Ask me if you are unsure about what is allowed.

Violations will result in severe penalties, including zero marks and disciplinary action.

9 A Note on Language and Transition

This course is taught in English, but we understand that this may be your first time learning advanced mathematics in a second language.

  • Listening – lectures will be delivered in clear and plain English, with key terms written on the board.
  • Reading – the textbook uses academic English; our lecture notes are written in simpler, more direct language to bridge the gap.
  • Writing – you are expected to submit assignments and exams in English (mathematical notation is universal!). We will provide model answers to help you learn the correct style.
  • Speaking – feel free to ask questions in class or during office hours in either English or Chinese – I am bilingual and happy to help you transition.

During the first few weeks, I will use some Chinese explanations to make sure everyone is on board, then gradually increase the English proportion.
My goal is to help you succeed – not to test your language skills.

Let’s have a great semester together!
Jiaye Xu