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This seminar was given in 2013 and is about maths notation, including set notation. Video and handouts are on the following page.

• Understanding maths notation seminar page

The MLC gave seminars on calculating with numbers, fractions and algebra in 2015, and all the videos are collected on the following page:

• Fundamental maths seminars page

This seminar was given in 2018 to students in a course called 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, which are not in Math Foundations for Biostats.)

The following mini-textbooksÌý are about various types of functions and contain explanations and practice exercises.

• Numbers and functions (PDF notes)ÌýÌý
• Linear functions (PDF notes)Ìý
• Quadratic functions (PDF notes)ÌýÌý
• Rational functions (PDF notes)Ìý
• Exponential functions (PDF notes)ÌýÌý
• Logarithmic functions (PDF notes)ÌýÌý
• Polynomial functions (PDF notes)ÌýÌý

This revision seminar was given for students in Intro to Financial Maths in 2018. The first hour discussed inverse functions and logarithms.

This revision seminar was given for students in Intro to Financial Maths in 2022. DavidÌýDavid discussed functions (at the start), including linear and quadratic functions, as well as inverse functions (56m11s).

This revision seminar was given to students in Intro to Financial Maths, and it began with a section on quadratic functions, including the various forms to write them and how to find solutions.

The following lecture was given for students in the MathTrackÌýbridging course, and it gives a lot of information about how polynomial functions work.

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 revision seminar was given to students in Mathematical Economics I in 2015 and it concerns limits and sign diagrams.

This revision seminar for Maths IA in Sem 1 2018 had a section on limits, including the various limit laws. The links below go straight to the right section, which starts at about 40 mins.

This seminar for Maths IB was given in Sem 2 2017 and had a section whichÌýcovered several examples of limits, starting at about 58 mins.Ìý

This seminar for Maths IB from Summer Semester 2023 started withÌýan example of calculating limits at infinity.

The following resources were created for the MLC bridging course MathsTrack, and might be helpful for understanding derivatives and maximisation of one-variable functions.

• Differentiation mini-textbookÌýÌý

• Applications of Differentiation mini-textbookÌýÌý

• Exponential and Logarithm Functions mini-textbookÌýÌý

In this seminar from Summer Semester 2019,ÌýDavid spent a lot of time talking about different ways to imagine multivariable functions and their derivatives.

This revision seminar was given to students of AQMF in 2013. David covered the idea of two-variable functions, their derivatives and an example of using Lagrange multipliers.

These lectures were given for the old MathsTrack bridging course, and discuss what integration is and techniques of integration.

• Topic 9: Integration textbook (PDF)Ìý

This revision seminar was given to students of the ³ÉÈË´óƬ course Mathematical Economics I in Semester 2 2021. David discussed the topic of integration, describing how he makes the decision of which technique to use and giving lots of examples of doing integrals.

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).

In Semester 2 2016, the MLC ran a revision seminar on improper integrals for Maths IA. David discussed what they are, and did several examples showing how to decide what to do. To watch the video or download the notes, follow the links below:

In Summer Semester 2017, the MLC ran another revision seminar on improper integrals for Maths IA, basically to go through some more difficult examples than in the previous seminar. To watch the video or download the notes, follow the links below:

This seminar for Probability & Statistics II students in semester 1 2016, wasÌýon bivariate distributions, specifically focussing on the decisions that need to be made in order to choose limits for integrals. David did three examples including finding the integral of the whole distribution, finding a probability, and finding a marginal distribution.

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, which I don't think is in Math foundations for Biostats).

This seminar in Semester 2Ìý2017 ended with a section which showed an overview of infinite series and Taylor series (starting at 1h21m).

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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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.

This revision seminar was given in Semester 1 2022 to students in Data Analytics I. David discussed probability,Ìýincluding terminologies such as "mutually exclusive", "exhaustive" and "independent".

This revision seminar was given to students ofÌýMathematics 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 of Probability & Statistics II in 2019 and it has a section on counting (starting at 1h36m40s).

This revision seminar for Business & Economic Statistics in 2013 was mainly on probability and distributions, including types of variables, probability distributions, theoretical means and standard deviations and probability laws. It also included a little on how to choose what hypothesis test goes with what situation, as well as the chi-squared test.

This revision seminar was given in Semester 1 2021 to students in Data Analytics I.ÌýDavid discussed probability, including probability distributions, (and also estimation and testing, which is not in Math Foundations for Biostats).

This revision seminar was given in 2018 for students in 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. (The list of distributions is likely to be different in Math Foundations for Biostats, so check with your notes.)

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This seminar for Probability & Statistics II in Semester 1 2021 began with a section on multivariate distributions, including conditional and marginal distributions and the multinomial distribution.

This seminar for Probability & Statistics II students in semester 1, 2018, hadÌýa section on bivariate distributions (starting atÌý1h28m20s).ÌýDavid talked through some of the ideas and did a couple of examples.

This short seminar for Probability & Statistics II students in Semester 1 2016 was about moment generating functions, including examples with both a discrete distribution and a continuous distribution. (I'm not sure if this is in too much detail for Math Foundations for Data Sci.)