Mathematical Foundations for Biostatistics
Resources for Mathematical Foundations for Biostatistics - for more information about the course, 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.
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 Math Foundations for Biostats 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 Math Foundations for Biostats 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 Math Foundations for Biostats exactly, so be sure to check your own course material if in doubt.)
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Notation, calculations and functions
This seminar was given in 2013 and is about maths notation, including set notation. Video and handouts are on the following page.
The MLC gave seminars on calculating with numbers, fractions and algebra in 2015, and all the videos are collected on the following 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.)
- 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)
The following mini-textbooks are about various types of functions and contain explanations and practice exercises.
- Numbers and functions (PDF notes)
- Linear functions (PDF notes)
- Quadratic functions (PDF notes)
- Rational functions (PDF notes)
- Exponential functions (PDF notes)
- Logarithmic functions (PDF notes)
- Polynomial functions (PDF notes)
This revision seminar was given for students in Intro to Financial Maths in 2018. The first hour discussed inverse functions and logarithms.
- Revision seminar section: inverse functions and logarithms 2018 (YouTube)
- Revision seminar section: inverse functions and logarithms 2018 (Echo360)
This revision seminar was given for students in Intro to Financial Maths in 2022. David David discussed functions (at the start), including linear and quadratic functions, as well as inverse functions (56m11s).
- Revision seminar video: functions 2022 (YouTube)
- Revision seminar video: functions 2022 (Echo360)
- Revision seminar notes: functions 2022 (PDF)
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.
- Revision seminar section: Quadratic functions, Sem 1 2021 (YouTube)
- Revision seminar section: Quadratic functions, Sem 1 2021 (Echo360)
The following lecture was given for students in the MathTrack bridging 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.
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Calculus: Limits
This revision seminar was given to students in Mathematical Economics I in 2015 and it concerns limits and sign diagrams.
- Revision seminar: Math Econ I: limits and sign diagrams 2015 (YouTube)
- Revision seminar: Math Econ I: limits and sign diagrams 2015 (Echo360)
- Revision seminar notes: Math Econ I: limits and sign diagrams 2015 (PDF)
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.
- Revision seminar section: limits, Sem 1 2018 (YouTube)
- Revision seminar section: limits, Sem 1 2018 (Echo360)
- Revision seminar notes: limits, Sem 1 2018 (PDF)
This seminar for Maths IB was given in Sem 2 2017 and had a section which covered several examples of limits, starting at about 58 mins.
- Revision seminar: limits examples, Sem 2 2017 (YouTube)
- Revision seminar: limits examples, Sem 2 2017 (Echo360)
- Revision seminar notes: limits examples, Sem 2 2017 (PDF)
This seminar for Maths IB from Summer Semester 2023 started with an example of calculating limits at infinity.
- Revision seminar video: Maths IB: Limits Summer 2023 (YouTube)
- Revision seminar video: Maths IB: Limits Summer 2023 (Echo360)
- Revision seminar notes: Maths IB: Limits at infinity Summer 2023 (PDF)
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Calculus: Derivatives and partial derivatives
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-textbook
- Differentiation lecture Part A: definitions and rules (YouTube)
- Differentiation lecture Part A: definitions and rules (Echo360)
- Desmos graph used in differentiation lecture part A
- Differentiation lecture Part B: tangents (YouTube)
- Differentiation lecture Part B: tangents (Echo360)
- Applications of Differentiation mini-textbook
- Applications of Differentiation lecture Part A: features of graphs (YouTube)
- Applications of Differentiation lecture Part A: features of graphs (Echo360)
- Desmos graph used in applications of differentiation lecture part A
- Applications of Differentiation lecture Part B: graph sketching examples (YouTube)
- Applications of Differentiation lecture Part B: graph sketching examples (Echo360)
- Applications of Differentiation lecture Part C: optimisation problems (YouTube)
- Applications of Differentiation lecture Part C: optimisation problems (Echo360)
- Exponential and Logarithm Functions mini-textbook
- Exponential and logarithmic functions lecture (YouTube)
- Exponential and logarithmic functions lecture (Echo360)
In this seminar from Summer Semester 2019, David spent a lot of time talking about different ways to imagine multivariable functions and their derivatives.
- Revision seminar: imagining multivariable functions, Summer 2019 (YouTube)
- Revision seminar: imagining multivariable functions, Summer 2019 (Echo360)
- Revision seminar notes: imagining multivariable functions Summer 2019 (PDF)
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.
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Calculus: Integration
These lectures were given for the old MathsTrack bridging course, and discuss what integration is and techniques of integration.
- Topic 9: Integration textbook (PDF)
- Integration lecture Part A: definitions (YouTube)
- Integration lecture Part A: definitions (Echo360)
- Integration lecture Part A handwritten notes (PDF)
- Integration lecture Part B: integration techniques (YouTube)
- Integration lecture Part B: integration techniques (Echo360)
- Integration lecture Part B handwritten notes (PDF)
- Integration lecture Part C: problem-solving (YouTube)
- Integration lecture Part C: problem-solving (Echo360)
- Integration lecture Part C handwritten notes (PDF)
This revision seminar was given to students of the University of Adelaide 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.
- Revision seminar: Math Econ I: integration 2021 (YouTube)
- Revision seminar: Math Econ I: integration 2021 (Echo360)
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)
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:
- Revision seminar: Improper integrals 2016 (YouTube)
- Revision seminar: Improper integrals 2016 (Echo360)
- Revision seminar notes: Improper integrals 2016 (PDF)
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:
- Revision seminar: Improper integrals 2017 (YouTube)
- Revision seminar: Improper integrals 2017 (Echo360)
- Revision seminar notes: Improper integrals 2017 (PDF)
This seminar for Probability & Statistics II students in semester 1 2016, was on 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.
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Calculus: Taylor series
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).
- 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 seminar in Semester 2 2017 ended with a section which showed an overview of infinite series and Taylor series (starting at 1h21m).
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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.)
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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.
- 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.
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Probability
This revision seminar was given in Semester 1 2022 to students in Data Analytics I. David discussed probability, including terminologies such as "mutually exclusive", "exhaustive" and "independent".
- Revision seminar video: probability Sem 1 2022 (YouTube)
- Revision seminar video: probability Sem 1 2022 (Echo360)
- Revision seminar notes: probability Sem 1 2022 (PDF)
This revision seminar was given to students of 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 2012 (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 of Probability & Statistics II in 2019 and it has a section on counting (starting at 1h36m40s).
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Random variables
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.
- Revision seminar: Stat Prac I: probability distributions, plus other stuff 2013 (YouTube)
- Revision seminar: Stat Prac I: probability distributions 2013, plus other stuff (Echo360)
- Revision seminar notes: Stat Prac I: probability distributions, plus other stuff 2013 (PDF)
This revision seminar was given in Semester 1 2021 to students in Data Analytics I. David discussed probability, including probability distributions, (and also estimation and testing, which is not in Math Foundations for Biostats).
- Revision seminar video: probability and estimation and testing Sem1 2021 (YouTube)
- Revision seminar video: probability and estimation and testing Sem1 2021 (Echo360)
This revision seminar was given in 2018 for students in 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. (The list of distributions is likely to be different in Math Foundations for Biostats, so check with your notes.)
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Multiple random variables
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.
- Revision seminar section: Prob & Stats II: multivariate distributions 2021 (YouTube)
- Revision seminar section: Prob & Stats II: multivariate distributions 2021 (Echo360)
This seminar for Probability & Statistics II students in semester 1, 2018, had a section on bivariate distributions (starting at 1h28m20s). David talked through some of the ideas and did a couple of examples.
- Revision seminar section: Prob & Stats II: bivariate distributions 2018 (YouTube)
- Revision seminar section: Prob & Stats II: bivariate distributions 2018 (Echo360)
- Revision seminar notes: Prob & Stats II: bivariate distributions 2018 (PDF)
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.)