Courses
MDE-MET-01; Calculus and Linear Algebra for Graduate Students
Course Details

MDE-MET-01: Calculus and Linear Algebra for Graduate Students

This site will be the primary source of information for this course.

Lectures

Lectures will take place in autumn 2024, on Wednesday mornings 9:45-11:00 and 11:15-12:30 at EH-4 (East Hall Classroom 4) IRC Seminar Room III.

An office hour can be arranged by appointment.

Course notes can be found here.

Recommendations for Preparation

There are no recommendations beyond reading the syllabus and the outline of the course.

Content and Educational Aims

This module offers a highly structured introduction to the fundamentals of two major pillars of mathematical modelling and analysis: single and multivariable calculus on the one hand and linear algebra on the other.

It is a gateway for graduate students who have not been exposed to the topics so far, or who would benefit from a refresher.

This course will focus on practical experience rather than on mathematical rigour.

Intended Learning Outcomes

Upon completion of this module, students will be able to

  1. Apply the fundamental concepts of calculus and linear algebra in structured situations
  2. Understand and use vectors and matrices, calculate determinants, eigenvalues and eigenvectors in simple cases
  3. Calculate derivatives and simple integrals
  4. Explain the importance of the methods of calculus and linear algebra in problems arising from applications
  5. Understand the methods of calculus and linear algebra used in more advanced modules as well as in scientific literature

The informal aim is to build intuition of some of the fundamental concepts in modern mathematics which are used in machine learning.

Indicative Literature

There is no primary or required course book, but there are many suitable books, such as:

  • “Introduction to Linear Algebra” - G. Strang (2016) Wellesley-Cambridge Press, 5th edition ISBN: 978-09802327-7-6.

Other useful resources are

  • “Linear Algebra and Learning from Data” - G. Strang (2019) Wellesley-Cambridge Press, ISBN: 978-06921963-8-0.
  • “Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares” - S. Boyd and L. Vandenberghe (2018) Cambridge University Press, ISBN: 978-1316518960.

Usability and Relationship to other Modules

  • The module is a non-mandatory remedial module of the Data Engineering MSc and an elective module Data Science for Society and Business MSc.

  • This module introduces and refreshes the essential calculus and linear algebra required in most of the modules of the data engineering program.

  • There is a placement test offered in the orientation week before the start of the first semester to help all students to find out if they need to take this course.

Course Outline

The following topics will be covered:

  • Vectors: addition of vectors and multiplication by a scalar, linear combinations, lengths and dot products
  • Matrices
  • Vector spaces, subspaces, column spaces, span, linear independence, basis. The nullspace of a matrix
  • Basis of the nullspace and the column space via Gaussian elimination. Free columns and pivot columns. Solutions of systems of linear equations
  • Rank of a matrix. Sum of the dimensions of the nullspace and the column space. Multiplication of matrices
  • Inverse of a matrix. Finding the inverse using Gaussian elimination
  • Orthogonality. Orthonormal bases, projections, and Gram-Schmidt
  • Determinants
  • Eigenvalues and eigenvectors
  • Diagonalization of a matrix
  • Symmetric matrices.
  • Principal Component Analysis
  • Derivatives, tangent lines, higher order derivatives, curve sketching.
  • Taylor series
  • Functions of several variables. Partial derivatives
  • Optimization problems. Positive/negative definite matrices
  • Jacobians and Hessians

Itinerary

Provisionally, the course will run as follows

gantt dateFormat MM-DD axisFormat %e-%b todayMarker off title Provisional Schedule 2024 section Linear Algebra Vectors :a1a, 09-02, 2w Assignment 1 : milestone, done, m1, 09-18, 0w Matrices :a1b, 09-16, 1w Linear equations :a1c, 09-23, 1w Assignment 2 : milestone, done, m2, 10-02, 0w Vector Spaces :a1d, 09-30, 1w Break :crit, 10-07, 1w Vector Spaces :a1e, 10-14, 1w Assignment 3 : milestone, m3, 10-21, 1d Matrices & Eigenvalues :a1f, 10-21, 3w Assignment 4 : milestone, active, m4, 11-01, 0d Assignment 5 : milestone, active, m5, 11-12, 0w section Calculus Single Variables :a2c, 11-11, 1w Taylor Series :a2d, 11-18, 1w Multiple Variables :a2e, 11-25, 1w Assignment 6 : milestone, active, m6, 11-23, 0w section Summary Summary :active, a3a, 12-02, 1w

Structure

The course content has the following structure:

---
markmap:
  zoom: false
  pan: false
---
- Linear Algebra
  - [Vectors](/docs/gradcalclinalg24/part1/vectors/)
  - [Matrices](/docs/gradcalclinalg24/part1/matrices/)
  - [Linear Equations](/docs/gradcalclinalg24/part2/linear-equations/)
  - [Vector Spaces](/docs/gradcalclinalg24/part1/spaces/)
  - [Matrices & Eigenvalues](/docs/gradcalclinalg24/part1/eigen/)
- Calculus
  - [Single Variable Calculus](/docs/gradcalclinalg24/part2/one-variable/)
  - [Taylor Series](/docs/gradcalclinalg24/part2/taylor/)
  - [Many Variable Calculus](/docs/gradcalclinalg24/part2/many-variables/)

Assessment

Examination Type
Examination Type: Module examination
Assessment Type: Written examination
Scope: All intended learning outcomes of this module
Duration: 120 min
Weight: 100%

You have three attempts to pass the module. Once you pass the module, no further retakes of the exam are possible. (See Academic Policies for more details.) The exams in this course are offered twice per year: in December and January.

No supplementary material can be brought to the exam. A calculator is necessary. Graphical and scientific calculators are permitted.

The pass mark is 45%.

Assignments

By submitting homework assignments, via Teams as a single pdf, you can improve this grade by up to 0.66 points, as bonus achievements.

Homework submission is voluntary although highly recommended. It is possible to get a 100% final grade without submitting homework or participating in quizzes.

Homework will be assigned every two weeks. Homework assignments are posted on here and on Teams approximately ten days before the due date.

You are encouraged to discuss homework between each other. However, the submitted assignments should be written individually. No copying is allowed!

The two lowest homework scores will be discarded before the final homework score is calculated. This rule covers short illness, excursions, late joining of the course, and similar situations.

Note that each homework assignment carries equal marks.

The problems on the final exam will be similar to the ones from homework. So, by doing homework you prepare for the final exam - maths is not a spectator sport.

Academic Integrity

All involved parties (lecturers, instructors and students) are expected to abide by the word and spirit of the “Code of Academic Integrity”. Violations of the Code should be brought to the attention of the Academic Integrity Committee.

Artifical Intelligence Use Policy

This policy covers any generative AI tool, such as ChatGPT, Elicit, etc. This includes text, slides, artwork/graphics/video/audio and other products.

  1. You are discouraged from using AI tools unless under direct instruction from your instructor to do so. Please contact your instructor if you are unsure or have questions before using AI for any assignment.

  2. Note that the material generated by these programs may be inaccurate, incomplete, or otherwise problematic. Their use may also stifle your own independent thinking and creativity. Accordingly, reduction in the grade is likely when using AI.

If any part of this AI policy is confusing or uncertain, please reach out to your instructor for a conversation before submitting your work.