Mathematics for Data Science / Mathematical Foundations of Data Science

Resources forÌýMathematics for Data Science IÌý²¹²Ô»å Mathematical Foundations ofÌýData Science - for more information about the courses, please seeÌýcourse 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:ÌýHigh School revision worksheets.

There are also mini textbooks and lecture videos covering much of the content from high school Maths Methods here:Ìýbridging course resources.Ìý

Also, thisÌýseminar pageÌýhas 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 ofÌýData 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.

    In 2014, David gave thisÌýrevision seminar for students in Maths 1A where he talked about finding domains and ranges for functions, as well as finding inverse functions.

    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.Ìý

  • 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.

    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.

    • 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.

      This revision seminar was given for students of Mathematics for Data ScienceÌýin Semester 2 2020. David discussed counting strategies, including the multiplication principle, and permutations and combinations.

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      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.

      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.

      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.

      This revision seminar was given in 2015 to students in the old course Business and Economic Statistics, andÌývarious ideas about probability including a discussion of how to think about probability using variables, and the meaning of disjoint and independent.ÌýÌý

      This revision seminar was given in 2018 for students in the old second year course Engineering Maths IIA.ÌýDavid 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.)Ìý

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    • 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.

      This lecture was given for students in the old MathsTrack bridging course in 2019. David discussed matrix inverses.

      ThisÌýlecture was given for students in the old MathsTrack bridging course in 2019. David discussed linear equations and row operations.

      This revision seminar given to students in Maths IM in 2014 covers matrix operations and also using matrices to solve linear equations.ÌýÌý

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      This seminar given to Maths IA in Sem 2 2017 had its firstÌýsection on determinants. It coveredÌýhow 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 beganÌýwith 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.)

      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.).

      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).

      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.

    • 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).

      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.

      This lecture was given forÌýstudents in the old MathsTrack bridging course in 2019. David discussed integration techniques including substitution and by parts.

      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.

      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.

      This seminar in Semester 2Ìý2017 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.

      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.

      2021

      Semester 2:ÌýDavid discussed conditional probability, then integrals and continuous random variables (starting at 1h6m30s).

      Semester 1:ÌýÌýDavid discussed Fermi estimation first, and then conditional probability (starting at 21m30s).

      2020

      Semester 2: David discussed counting strategies, including the multiplication principle, and permutations and combinations.

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