Mathematics for Data Science / Mathematical Foundations of Data Science
Resources for Mathematics for Data Science I and Mathematical Foundations of Data Science - for more information about the courses, please see course outlines.
Preparation and Study Skills
We have revision worksheets on a number of topics, that will help you revise topics from high-school maths. These are available in print form from the MLC room in Hub Central, but you can also download them here: High School revision worksheets.
There are also mini textbooks and lecture videos covering much of the content from high school Maths Methods here: bridging course resources.
Also, this seminar page has two seminars giving advice on studying for a course like this that has lots of maths and an exam.
Maths Drop-In Centre
Students in Maths for Data Science and Math Foundations of Data Science are allowed and encouraged to use the MLC Drop-In Centre to discuss any aspect of their mathematical learning. The Drop-In Centre is available both face-to-face and online, and you can find out more on the MLC Drop-In Centre website.
Resources
The MLC has given lectures on the topics involved in Maths for Data Science to students in various courses over the years. Links to these seminars and related resources are organised below. (Note that sometimes the content will not match Maths for Data Science exactly, so be sure to check your own course material if in doubt.)
-
Notation and calculations
This seminar was given in 2013 and is about maths notation, including set notation.
This seminar was given in 2018 to students in Maths 1M on various special functions that it will be useful to know for this course. David talked about piecewise functions and composing them to make new functions. He also talked about how to compose trig functions and inverse trig functions.
- Revision seminar section: Maths IM: special functions, Sem 1 2018 (YouTube)
- Revision seminar section: Maths IM: special functions, Sem 1 2018 (Echo360)
- Revision seminar notes: Maths IM: special functions, Sem 1 2018 (PDF)
In 2014, David gave this revision seminar for students in Maths 1A where he talked about finding domains and ranges for functions, as well as finding inverse functions.
- Revision seminar: Maths IA: domains and ranges 2014 (YouTube)
- Revision seminar: Maths IA: domains and ranges 2014 (Echo360)
- Revision seminar notes: Maths IA: domains and ranges 2014 (PDF)
In Semester 1 2021, David gave a revision seminar for students in Math Foundations for Data Science that started with a section on Fermi Estimation.
-
Sum notation and series
This seminar for Maths 1A in Sem 1 2016 discussed how sum notation works, the rules for how it interacts with other operations, and some of the special manipulations you can do with it.
- Revision seminar: sum notation, Sem 1 2016 (YouTube)
- Revision seminar: sum notation, Sem 1 2016 (Echo360)
- Revision seminar notes: sum notation, Sem 1 2016 (PDF)
This handout lists the various tests for convergence, as well as showing the process of finding an interval of convergence.
This seminar for Maths 1B in Semester 2 2018 was recorded in two parts. At the end of the first part (at 32m38s), David started talking about infinite series, and then continued in the second part.
- Revision seminar section: series Semester 2 2018 part I (YouTube)
- Revision seminar section: series Semester 2 2018 part I (Echo360)
- Revision seminar: infinite series Semester 2 2018 part II (YouTube)
- Revision seminar: infinite series Semester 2 2018 part II (Echo360)
- Revision seminar notes: infinite series Sem 2 2018 (PDF)
-
Counting and Probability
This revision seminar was given to students of the old course Mathematics for Information Technology in 2012. It covered counting techniques, including combinations, permutations, allocations etc.
- Revision seminar: Maths for IT: counting techniques 2012 (YouTube)
- Revision seminar: Maths for IT: counting techniques 2012 (Echo360)
- Revision seminar notes: Maths for IT: counting techniques (PDF)
This revision seminar was given for students of Mathematics for Data Science in Semester 2 2020. David discussed counting strategies, including the multiplication principle, and permutations and combinations.
- Revision seminar: Maths for Data Science: counting techniques 2020 (YouTube)
- Revision seminar: Maths for Data Science: counting techniques 2020 (Echo360)
This revision seminar was given to students in the old course Maths for Information Technology in 2017, and it had a section on conditional probability.
- Revision seminar section: Maths for IT: conditional probability 2017 (YouTube)
- Revision seminar section: Maths for IT: conditional probability 2017 (Echo360)
- Revision seminar notes: Maths for IT: conditional probability (PDF)
This revision seminar was given for students in Mathematical Foundations of Data Science in Semester 1 2021, and had a section on conditional probability (starting at 21m30s), where David did a couple of examples of solving problems involving conditional probability.
- Revision seminar: Math Foundations for Data Sci: conditional probability Sem 1 2021 (YouTube)
- Revision seminar: Maths Foundations for Data Sci: conditional probability Sem 1 2021 (Echo360)
This revision seminar was given for students in Maths for Data Science / Math Foundations of Data Science in Semester 2 2021, and started with a section on conditional probability.
- Revision seminar: Maths for Data Sci: conditional probability Sem 2 2021 (YouTube)
- Revision seminar: Maths for Data Sci: conditional probability Sem 2 2021 (Echo360)
This revision seminar was given in 2015 to students in the old course Business and Economic Statistics, and various ideas about probability including a discussion of how to think about probability using variables, and the meaning of disjoint and independent.
- Revision seminar video: BES: probability 2015 (YouTube)
- Revision seminar video: BES: probability 2015 (Echo360)
- Revision seminar notes: BES: probability 2015 (PDF)
This revision seminar was given in 2018 for students in the old second year course Engineering Maths IIA. David discussed all of the distributions appearing in Eng Maths IIA in turn, including how to decide which distribution you want to use and how to use it. (Not all of these distributions are in Maths for Data Science / Math Foundations of Data Science, but the seminar might still be useful.)
-
Matrices and linear equations
This lecture was given for students in the old MathsTrack bridging course in 2019. David discussed matrix operations such as addition, multiplication and transpose.
- Lecture: MathsTrack: matrix operations 2019 (YouTube)
- Lecture: MathsTrack: matrix operations 2019 (Echo360)
- Lecture notes: MathsTrack: matrix operations 2019 (PDF)
This lecture was given for students in the old MathsTrack bridging course in 2019. David discussed matrix inverses.
- Lecture: MathsTrack: matrix inverses 2019 (YouTube)
- Lecture: MathsTrack: matrix inverses 2019 (Echo360)
- Lecture notes: MathsTrack: matrix inverses 2019 (PDF)
This lecture was given for students in the old MathsTrack bridging course in 2019. David discussed linear equations and row operations.
- Lecture: MathsTrack: linear equations 2019 (YouTube)
- Lecture: MathsTrack: linear equations 2019 (Echo360)
- Lecture notes: MathsTrack: linear equations 2019 (PDF)
This revision seminar given to students in Maths IM in 2014 covers matrix operations and also using matrices to solve linear equations.
- Revision seminar: Maths IM: linear equations, 2014 (YouTube)
- Revision seminar: Maths IM: linear equations, 2014 (Echo360)
- Revision seminar notes: Maths IM: linear equations 2014 (PDF)
This seminar given to Maths IA in Sem 2 2017 had its first section on determinants. It covered how to calculate determinants, how they're related to various other matrix calculations, and how row operations affect them.
-
Linear dependence and eigenvalues
This seminar for Maths IA from Sem 1 2017 began with a section on linear dependence. (Note David mentions the concept of "span" here, which is not explicitly mentioned in Maths for Data Sci, but the rest of the seminar is still useful.)
- Revision seminar section: Maths IA: linear dependence, Sem 1 2017 (YouTube)
- Revision seminar section: Maths IA: linear dependence, Sem 1 2017 (Echo360)
- Revision seminar notes: Maths IA: linear dependence, Sem 1 2017 (PDF)
This seminar for Maths IA from 2012 covers eigenvalues and eigenvectors for matrices. (Note again it mentions span and subspaces, but the rest of the content is relevant to Maths for Data Sci.).
- Revision seminar: Maths IA: eigenvalues 2012 (YouTube)
- Revision seminar: Maths IA: eigenvalues 2012 (Echo360)
- Revision seminar notes: Maths IA: eigenvalues 2012 (PDF)
This PDF handout list various facts about eigenvalues and some examples of classic problems using them (only the first two pages are relevant to Maths for Data Science).
This seminar for Maths IA from Semester 2 2017 has a section about dynamical system long term behaviour (starting at 49m20s).
- Revision seminar section: Maths IA: dynamical systems, Sem 2 2017 (YouTube)
- Revision seminar section: Maths IA: dynamical systems, Sem 2 2017 (Echo360)
- Revision seminar notes: Maths IA: dynamical systems, Sem 2 2017 (PDF)
This revision seminar was given for Maths for Data Science in Semester 2 2022, and the second half (starting at 43m37s) discussed eigenvectors and using them to predict a long term process.
- Revision seminar section: Maths for Data Sci, eivenvectors and long term behaviour Sem 2 2022 (YouTube)
- Revision seminar section: Maths for Data Sci, eigenvectors and long term behaviour Sem 2 2022 (Echo360)
- Revision seminar notes: Maths for Data Sci, eigenvectors and long term behaviour Sem 2 2022 (PDF)
-
Calculus and Taylor polynomials
This revision seminar was given for students in Maths for Data Science / Math Foundations of Data Science in Semester 2 2021, and had a section on integration and continuous probability distributions (starting at 1h6m30s).
- Revision seminar section: Maths for Data Sci: integration Sem 2 2021 (YouTube)
- Revision seminar section: Maths for Data Sci: integration Sem 2 2021 (Echo360)
This lecture was given for students in the old MathsTrack bridging course in 2019. David discussed definitions for derivatives and rules for calculating derivatives. Also the Desmos graph he used in the lecture is linked below.
- Lecture: MathsTrack: Differentiation definitions and rules (YouTube)
- Lecture: MathsTrack: Differentiation definitions and rules (Echo360)
- Lecture notes: MathsTrack: Differentiation definitions and rules (PDF)
- Desmos graph used in differentiation lecture
This lecture was given for students in the old MathsTrack bridging course in 2019. David discussed integration techniques including substitution and by parts.
- Lecture: MathsTrack: Integration techniques (YouTube)
- Lecture: MathsTrack: Integration techniques (Echo360)
- Lecture notes: MathsTrack: Integration techniques (PDF)
This seminar for students in Maths IB in Summer Semester 2019 gave an intro into what Taylor series and Taylor polynomials are, then gave several examples of finding them and working with the error formula.
- Revision seminar: Taylor polynomials, series and errors Summer 2019 (YouTube)
- Revision seminar: Taylor polynomials, series and errors, Summer 2019 (Echo360)
- Revision seminar notes: Taylor polynomials, series and errors, Summer 2019 (PDF)
This revision seminar was given for students in Maths for Data Science in Semester 2 2022, and started with a section on Taylor polynomials and their errors/remainders.
- Revision seminar section: Maths for Data Sci: Taylor polynomials, Sem 2 2022 (YouTube)
- Revision seminar section: Maths for Data Sci: Taylor polynomials, Sem 2 2022 (Echo360)
- Revision seminar notes: Maths for Data Sci: Taylor polynomials Sem 2 2022 (PDF)
- Desmos graph made during the Taylor polynomials seminar Sem 2 2022 (website)
This seminar in Semester 2 2017 ended with a section which showed an overview of infinite series and Taylor series (starting at 1h21m).
-
Revision seminars in order of time
These are the revision seminars that have been given for this course since its creation in 2020.
2023
Semester 2: Nicholas discussed various topics, doing several miscellaneous problems.
- Revision seminar video: Maths for Data Sci, Sem 2 2023 (YouTube)
- Revision seminar video: Maths for Data Sci, Sem 2 2023 (Echo360)
- Revision seminar notes: Maths for Data Sci, Sem 2 2023 (PDF)
2022
Semester 2: David discussed Taylor polynomials and their errors/remainders, and then (starting at 43m37s) discussed eigenvectors and using them to predict a long term process.
- Revision seminar video: Maths for Data Sci, Sem 2 2022 (YouTube)
- Revision seminar video: Maths for Data Sci, Sem 2 2022 (Echo360)
- Revision seminar notes: Maths for Data Sci: Taylor polynomials Sem 2 2022 (PDF)
- Desmos graph made during the Taylor polynomials seminar Sem 2 2022 (website)
- Revision seminar notes: Maths for Data Sci: predicting with eigenvectors Sem 2 2022 (PDF)
2021
Semester 2: David discussed conditional probability, then integrals and continuous random variables (starting at 1h6m30s).
- Revision seminar: Maths for Data Sci: Sem 2 2021 (YouTube)
- Revision seminar: Maths for Data Sci: Sem 2 2021 (Echo360)
Semester 1: David discussed Fermi estimation first, and then conditional probability (starting at 21m30s).
- Revision seminar: Math Foundations for Data Sci: Sem 1 2021 (YouTube)
- Revision seminar: Math Foundations for Data Sci: Sem 1 2021 (Echo360)
2020
Semester 2: David discussed counting strategies, including the multiplication principle, and permutations and combinations.