This course has a heavy focus on some of the mathematics used in data science applications. It is a linear algebra course that also incorporates some multi-variable calculus. The foundations of linear algebra are studied and explored with the help of numerical examples from the Julia programming language. The assignments and final project also celebrate these 12 data science use cases:
- Clustering
- Convergence proof for the perceptron
- Least squares data fitting
- Least squares classification
- Multi-objective least squares and regularization
- Multiple ways for evaluating least squares
- Linear dynamical systems and systems of differential equations
- Covariance matrices and joint probabilities
- Multi-variate Gaussian distributions and weighted least squares
- Cholesky decomposition for multi-variate random variable simulation
- Analysis of gradient descent and extensions
- Principal component analysis (PCA)
Background: The prerequisite for the course is knowledge comparable to
MATH7501. This includes basic discrete mathematics, calculus and elementary manipulation of vectors and matrices. Feel free to use the
7501 - course reader to brush-up as needed. If you haven't done MATH7501, you may also use the
mathematics first year learning centre to get help on elementary (MATH7501'ish) items such as basic matrix/vector operations, basic calculus, basic understanding of mathematical notation. It is also recommended that you read the following sections from the [VMLS] book as background: 1.1, 1.2, 1.3, 1.4, 3.1, 3.2, 6.1, 6.2, 6.3, 6.4, 7.1, 7.2, 7.3, 10.1, 10.2, 10.3.
The course makes use of the following resources and materials:
References to [CLAWJ], [DSUC], [JULIA], [VMLS], [LALFD], [ILA], [3B1B], and [SWJ], are frequently made during the course and in each week students are requested to cover selected material from these sources.
The course assessment includes two assignments, three quizzes, and a final project:
Quiz, assignment, and project submission information: All assessment items are to be submitted to
mathdatasciencebridgingsubmissions@uq.edu.au (this account should not be used for any queries - only for submissions). Submissions should include two files, a PDF file and an audio clip. The submission must adhere to the following guidelines:
- Submit a single PDF file, with pages of uniform size, and a file size that does not exceed 8MB (you can use a pdf compression utility if needed). The name of the PDF file should be FFFF_LLLL_SN-IIII.pdf where FFFF is your first name, LLLL, is your last name, SN is your student number, and IIII is "Quiz1", "Assignment1", "Project", etc.
- Do not submit code - instead format your code into the PDF file.
- Both handwritten notes and typed notes are acceptable. However typed (LaTeX/Jupyter) mathematics is preferable.
- All graphs, plots, source code, and other figures must be clearly labeled.
- All questions/items must appear in order.
- A recorded audio clip in any standard format with a minimum duration of one minute and a maximum duration of two minutes. The file size may note exceed 4MB. In your recording, state your name, and your experience with this assignment. Mention the resources that you used to carry out the assignment, and if valid, indicate that you did not plagiarize. Name the audio clip in the same way that your PDF file is named, but with the valid audio format extension.