Course notes

Course notes

This page contains links to notes and resources that we use in our courses and that are also helpful for your study.

Bridging Course Text:

The first is a link to the modules that we use for our mathematics bridging courses and are available for downloading as pdf files. These are called the MUMS modules. They are suitable for bridging to NSW Advanced and Advanced plus Extension 1 Mathematics. We hope that you find them useful. The MUMS Modules are available to purchase. You can purchase the books by dropping into the centre any day of the week during semester or completing the order form.

MUMS Modules - Text for Bridging Courses

Each Macquarie University Mathematical Skills (MUMS) module begins with a short diagnostic test (onetwo, three and four). These tests should help you decide whether you need to work through entire modules, or just individual chapters. The documents below are in pdf: a small increase in magnification may be needed to display all formulae and graphics correctly. All suggestions and corrections are welcome.

If you would like to purchase one or all of these books please clink on the following link:

MUMS Order Form

Please note: that when you access some chapters a zipped file will need to be downloaded. This is because the chapter has short videos attached to some examples. To view the chapter with videos, download and save the zipped file onto your computer, then unzip the file and click on the pdf inside. You will need to view the pdf in Adobe Acrobat Reader to see the videos.

We greatly appreciate your feedback on the videos.

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Module One

1.1 Order of Operations 1.6 Signed Numbers
1.2 Factorisation of Integers 1.7 Further Signed Numbers
1.3 Fractions 1.8 Power Laws
1.4 Fractions and Decimals 1.9 Introduction to Algebra
1.5 Percentages 1.10 Further Algebra

Module Two

2.1 Factors of Algebraic Expressions 2.6 Factorizing Algebraic Expressions
2.2 Solving Equations in One Variable 2.7 Logarithms and Exponentials
2.3 Algebraic Fractions 2.8 Introduction to Trigonometry
2.4 Introduction to Inequalities 2.9 Introduction to the Cartesian Plane
2.5 Arithmetic with Surds  

Module Three

3.1 Functions 3.6 Arithmetic and Geometric Progressions
3.2 Graphs 3.7 Continuity and Limits
3.3 Trigonometry 3.8 Introduction to Differentiation
3.4 Further Trigonometry 3.9 Further Differentiation
3.5 Simultaneous Equations 3.10 Differentiating Special Functions

Module Four

4.1 More Differentiation 4.7 Modifying Functions
4.2 Introduction to Integration 4.8 Composite and Inverse Functions
4.3 Integrating Special Functions 4.9 Exponentials and Logarithms
4.4 Applications of Integration 4.10 Sigma Notation
4.5 Polynomials 4.11 Counting
4.6 Properties of Trigonometric Functions 4.12 The Binomial Theorem
 4.13 Induction

© Macquarie University 2015

This material is available free to all individuals, on the understanding that it is not to be used for financial gains, and may be downloaded and/or photocopied, with or without permission from the authors. However, this material may not be kept on any information storage and retrieval system without permission from the authors, unless such system is not accessible to any individual other than its owners.

Other Useful Notes:

Lecture Notes in Mathematics

The course notes that were previously used for first year mathematics courses at Macquarie University are available at this site as are other notes written by Dr William Chen.

Dilshara's Maths Notes

These are Dilshara's Notes from her first year lectures in Math130. They are suitable for bridging to NSW Advanced Mathematics.

Short Course Notes:

Tutorials:

How to study maths

1. Take notes in lectures

Take good lectures notes – ones which you could refer to later. Your lecturer may not necessarily write down everything he/she says so you may like to add to the standard lecture notes by including snippets of what is being said as well.

2. Make Summaries

Summarise each topic you study using your lecture notes and related texts. You can do this by referring to the lecture notes you took in lectures and presenting it as a summary. All the main points should be there. You may need to refer to textbooks to consolidate some of the material. A summary does not have to be short – you can include examples and as much working as you like. This will become your reference book – a quick review of what you are expected to know in your course of study. Summaries take a while to do but it is worth it in the end.

3. Refer to textbooks

Textbooks are an additional resource to your lecture notes. Often a topic may be expanded on in more detail in your textbook with additional examples given. When you make your summaries have your textbook open at your topic and use it as a reference and guide.

4. Do and redo as many exercises as you can find

This is probably the most helpful way of studying maths – to do and redo as many exercises that you can find. Use your tutorial exercises as a guide but also refer to your textbook and recommended reading lists. Find the topic that you are working on and do as many exercises that you can on it.

5. Ask questions (especially if you are stuck)

The best way of getting help with maths is face to face. Don’t be scared of asking your lecturer or tutor for help. Spend time at the Numeracy Centre (or your Maths Study Centre) where tutors are available to give you individual help. Discuss your questions with your friends and maybe together you can come up with a solution.

6. Work through all your tutorial exercises and assignments

Redoing your assignments is important especially before an exam as it gives you an idea of the standard of knowledge you are required to have.

For more of a discussion on this topic, the following site has some excellent information: Paul’s Online Notes

Measurement tutorial

An interactive collection of World Wide Web pages designed to help science students come to grips with the details of measuring things.

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