Statistics & Numerical Methods II
Resources for the course Statistics & Numerical Methods II - for more information about the course, please see course outlines.
MLC Drop-In Centre
Students from Statistics & Numerical Methods II can use the drop-in centre, but we will give priority to first year students. If you see every other table has students, then we would appreciate it if you found another place to sit so that there is room for new students.
Please note that not every staff member in the MLC knows all of the content in Statistics & Numerical Methods II, there will be times when we can only give general study advice for this course. Note also that we are usually not able to give help with fixing MATLAB code.
Resources for Stats & Numerical Methods II
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Assumed Knowledge
Polynomials
Polynomials are used in Numerical Methods for approximating functions. It's good to have an understanding of how they behave. This lecture on Polynomials from the old MathsTrack bridging course will help you revise the behaviour of polynomials.
- VIDEO (YouTube): MathsTrack lecture: polynomials lecture 2019
- VIDEO (Echo360): MathsTrack lecture: polynomials lecture 2019
Taylor's theorem
Taylor's theorem is used in Numerical Methods to figure out errors in methods of approximation.
This seminar for Maths IB students 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.
- VIDEO (YouTube): Maths IB revision seminar: Taylor polynomials, series and errors Summer 2019
- VIDEO (Echo360): Maths IB revision seminar: Taylor polynomials, series and errors, Summer 2019
- PDF: Maths IB: Taylor series and errors 2019
This revision seminar for Maths IB students from 2016 was specifically about the Taylor error formula.
- VIDEO (YouTube): Maths IB revision seminar: Taylor polynomial errors 2016
- VIDEO (Echo360): Maths IB revision seminar: Taylor polynomial errors 2016
- PDF: Maths IB: Taylor polynomial errors 2016
Integration
Numerical Methods covers ways to approximate integrals for functions you don't know. This is based on the idea of an average value using integration. This lecture from the old MathTrackX bridging course introduces integration specifically from the perspective of average values, and may help you to revise your understanding of integration.
- VIDEO (YouTube): MathsTrack lecture: integration definitions 2019
- VIDEO (Echo360): MathssTrack lecture: integration definitions 2019
Matrices and row operations
Solving linear equations is something that is discussed in Numerical Methods, and row operations are an explanation for why some of the methods work. This revision seminar was given for students in Maths IA in 2014 and covers matrix operations and also using matrices to solve linear equations (the linear equations section begins at about 58 mins).
- VIDEO (YouTube): Maths IA revision seminar: matrices and linear equations, 2014
- VIDEO (YouTube): Maths IA revision seminar: matrices and linear equations, 2014
Orthogonal matrices are one of the tools that are used to help solve equations in Numerical Methods. This revision seminar was given for students in Maths IB in 2020 and begins with a section on orthogonal matrices.
- VIDEO (YouTube): Maths IB revision seminar: orthogonal matrices, Semester 2 2020
- VIDEO: (Echo360): Maths IB revision seminar: orthogonal matrices, Semester 2 2020
Newton's method and Euler's method
One technique in Numerical Methods is Newton's Method (also known as the Newton-Raphson method). This revision seminar for Maths IB from 2016 covered the use of Newton's method (and the bisection method) to find solutions of equations.
- VIDEO (YouTube): Maths IB revision seminar: Newton's method and bisection method 2016
- VIDEO (Echo360): Maths IB revision seminar: Newton's method and bisection method 2016
- PDF: Maths IB: Newton and bisection method notes 2016
Euler's method is an approximate way to solve a specific kind of differential equation. In this revision seminar for Maths IM from Semester 2 2020, there was a section on Euler's method (starting at 35m).
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Resources for Statistics
The course Statistics & Numerical Methods was created in 2020. Before that was a course called Engineering Mathematics IIA, which included much of the same statistics content. The resources below were mostly created for Eng Maths IIA, but should be useful for making sense of the statistics content in Stats & Numerical Methods.
In 2022, David gave a revision seminar to Stats & Numerical Methods II students whose second part was about test statistics (starting at 1h6m50s).
- VIDEO (YouTube): Stats & Numerical Methods II: test statistics 2022
- VIDEO (Echo360): Stats & Numerical Methods II: test statistics 2022
- PDF: Stats & Numerical Methods II: test statistics notes 2022
In 2023, David gave a revision seminar to Stats & Numerical Methods II students whose second part was about choosing the right probability distribution, both for regular probability and for statistical tests (starting at 31m50s).
- VIDEO (YouTube): Stats & Numerical Methods II: Choosing distributions 2023
- VIDEO (Echo360): Stats & Numerical Methods II: Choosing distributions 2023
- PDF: Stats & Numerical Methods II: choosing distributions notes 2023
In 2021, David gave a revision seminar to Stats & Numerical Methods II students about the various hypothesis tests in the course that year, including the two chi-squared tests.
- VIDEO (YouTube): Stats & Numerical Methods II: hypothesis tests 2021
- VIDEO (Echo360): Stats & Numerical Methods II: hypothesis tests 2021
In 2019, David gave a revision seminar to Eng Maths IIA students with a section on choosing what stats test to use (the section starts at 1h2m).
- VIDEO (YouTube): Eng Maths IIA revision seminar section: choosing the right stats 2019
- VIDEO (Echo360): Eng Maths IIA revision seminar section: choosing the right stats 2019
- PDF: Eng Maths IIA: choosing stats notes 2019
In 2018, David gave a revision seminar on probability distributions to students in Eng 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. (Note the list of distributions may be a bit different in Statistics & Numerical Methods II.)
- VIDEO (YouTube): Eng Maths IIA revision seminar: probability distributions 2018
- VIDEO (Echo360): Eng Maths IIA revision seminar: probability distributions 2018
- PDF: Eng Maths IIA probability distributions notes 2018
In 2017, David gave a revision seminar to Eng Maths IIA students with a part on linear regression (this part starts at 1h12m45s).
- VIDEO (YouTube): Eng Maths IIA revision seminar: regression 2017
- VIDEO (Echo360): Eng Maths IIA revision seminar: regression 2017
- PDF: Eng Maths IIA regression notes 2017
In 2016, David gave a revision seminar to Eng Maths IIA students with some details about statistics and probability. You may find some of the advice about choosing between hypothesis tests and choosing between probability distributions useful. (Note the list of hypothesis tests may be slightly different than that used in the new course.)
- VIDEO (YouTube): Eng Maths IIA revision seminar: hypothesis tests 2016
- VIDEO (Echo360): Eng Maths IIA revision seminar: hypothesis tests 2016
- PDF: Eng Maths IIA hypothesis tests notes 2016
- VIDEO (YouTube): Eng Maths IIA revision seminar: probability distributions 2016
- VIDEO (Echo360): Eng Maths IIA revision seminar: probability distributions 2016
- PDF: Eng Maths IIA probability distributions notes 2016
In 2012, David gave a revision seminar to students in Eng Maths IIA about statistics and probability. He covered confidence intervals and assumption-checking for regression, some probability distributions, and some hypothesis testing. (Note the exam formula sheet used may be different to what is available in this course now, so be careful.):
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Resources for Numerical Methods
Some methods for approximating integrals are the trapezoidal rule and Simpson's rule, which used to be part of the Maths IA curriculum. This revision seminar was given for Maths IA students in 2017, and it contained a section on the trapezoidal rule and Simpson's rule and their errors (starting at 1h41m). (Note the error formulas might be a bit different to the ones in Stats & Numerical Methods, but the ideas are similar.)
- VIDEO (YouTube): Maths IA revision seminar section: trapezoidal and Simpson's rules 2017
- VIDEO (Echo360): Maths IA revision seminar section: trapezoidal and Simpson's rules 2017
- PDF: Maths IA trapezoidal and Simpson's rules 2017
The revision seminar for Statistics & Numerical Methods II in Semester 2 2022 started with discussion of using Taylor's theorem for the errors in numerical derivatives (at the start), and then Simpson's rule (starting at 58m).
- VIDEO (YouTube): Stats & Numerical Methods II: numerical derivatives and Simpson's rule 2022
- VIDEO (Echo360): Stats & Numerical Methods II: test statistics 2022
- PDF: Stats & Numerical Methods II: numerical derivative errors 2022
- PDF: Stats & Numerical Methods II: Simpson's rule 2022
This revision seminar for Statistics & Numerical Methods II in Semester 2 2023 started with discussion on what Big O notation is trying to do, both with graphs and tables, and also with algebra.
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Revision seminars in order of time from 2021
2023
In Semester 2 2023, David discussed various aspects of Big O notation (at the start), and then how to choose which distribution you should use both in the wild and during hypothesis testing (starting at 31m50s).
- VIDEO (YouTube): Stats & Numerical Methods II: big O notation 2023
- VIDEO (Echo360): Stats & Numerical Methods II: big O notation 2023
- PDF: Stats & Numerical Methods II: big O notation notes 2023
- PDF: Stats & Numerical Methods II: choosing distributions notes 2023
2022
In Semester 2 2022, David discussed Taylor's theorem for the errors in numerical derivatives (at the start), and Simpson's rule (starting at 58m), and test statistics (starting at 1h6m50s).
- VIDEO (YouTube): Stats & Numerical Methods II: numerical derivatives and Simpson's rule 2022
- VIDEO (Echo360): Stats & Numerical Methods II: test statistics 2022
- PDF: Stats & Numerical Methods II: numerical derivative errors 2022
- PDF: Stats & Numerical Methods II: Simpson's rule 2022
- PDF: Stats & Numerical Methods II: test statistics 2022
2021
In Semester 2 2021, David gave a revision seminar to Stats & Numerical Methods II students about the various hypothesis tests in the course that year, including the two chi-squared tests.