These resources are meant to complement (not replace) your lectures and tutorials. Some things may be explained differently or use different notation – if you are unsure of where to start or what to read then please get in touch and we will be happy to help!

The Maths Gym, in collaboration with SCHOLAR, have produced an online resource which covers many foundational topics that are key to a strong grounding in mathematics and statistics.

Each topic consists of a combination of key points, worked examples, interactive activities, exercises, short instructional videos and the opportunity to self-test. You can follow the whole course or dip into topics as needed.

See our introduction video for a quick tour of the resource.

Access is available to anyone with a Heriot Watt University email address and can be found here.

## Mathematics for Success

This course covers many fundamental topics and is open to anyone who wishes to use it – see full details below!

“Mathematics for Success” is an interactive self-paced university-preparation course which aims to bridge the mathematics requirements into Heriot-Watt (Malaysia) program. The course consists of five essential mathematical chapters, where each chapter comprises a few modules. For each module, there are three designed activities, namely pre-recorded videos, reading materials as well as some exercises helping students to master the topic.

Please send an email to k.ong@hw.ac.uk (Dr. Ong Kai Lin) and express your interest. The course was created in a VLE platform called Open Learning.

Chapter 1: Functions

• 1.1 Introduction to functions
• 1.2 Composite and inverse functions
• 1.3 Exponential and logarithmic functions

Chapter 2: Differential calculus

• 2.1 Introduction to differential calculus
• 2.2 Product and quotient rules
• 2.3 Chain rule and combination of differentiation rules
• 2.4 Higher order derivatives
• 2.5 Implicit differentiation
• 2.6 Application: sketching functions
• 2.7 Numbas practices

Chapter 3: Integral calculus

• 3.1 Introduction to integral calculus
• 3.2 Integration using partial fractions
• 3.3 Integration by parts
• 3.4 Integration by substitution
• 3.5 Application: differential equations
• 3.6 Numbas practices

Chapter 4: Complex numbers

• 4.1 Introduction to complex numbers
• 4.2 Basic arithmetic of complex numbers and Argand diagram
• 4.3 Modulus, argument and polar form
• 4.4 Exponential form
• 4.5 Numbas practices

Chapter 5: Sequences and series

• 5.1 Introduction to sequences and series
• 5.2 Infinite series, partial sums and sum to infinity
• 5.3 Binomial series
• 5.4 Recurrence relations
• 5.5 Numbas practices

## External Websites

#### These websites cover a variety of topics

• HELM booklets are an extensive set of booklets covering many topics in mathematics and statistics – they are aimed at engineers and scientists. Each booklet has notes, worked examples and exercises.
• The mathcentre is a wonderful resource organised into many different topics and applications. There is a combination of notes, videos, example and quizzes.
• Khan Academy is a site based on the American school system and covers topics from pre-school to early university level. This also has a combination of notes, videos, examples and quizzes.
• The statstutor pages lead you through many common statistical topics with a selection of notes, videos, examples and quizzes.
• NRich has resources to prepare you for university mathematics and the use of mathematics in different subjects at university e.g. engineering, biology, chemistry and physics. These pages recap school mathematics for specific subjects.