# Bridging course

The Bridging Course modules have been specifically designed to cover the prerequisite knowledge required to undertake First-Year maths courses.

## Overview

### What are Maths Bridging Course Modules?

The Bridging Course modules have been specifically designed to cover the prerequisite knowledge required to undertake the following First-Year maths courses:

- Mathematics and Applications 1 (MATH1003) or Discrete Mathematical Models (MATH1005/MATH6005)
- Mathematics and Applications 1 (MATH1013)
- Advanced Mathematics and Applications 1 (MATH1115)
- Mathematical Foundations for Actuarial Studies (MATH1113)

### Who should enrol in the Bridging Course modules?

- Students who are required to take one of the First-Year maths courses above as part of their degree program, but who do not have the prerequisite knowledge, are required to complete one or more of the bridging modules.
- Students who have the prerequisites but would like a refresh their knowledge, are welcome to enrol in the bridging modules.

### Diagnostic Test

**Please note: It is mandatory for students to complete the diagnostic test prior to enrolling in any of the Bridging Modules.**

**Which Maths Bridging Module(s) should students take?**

A diagnostic test is available to help students determine which module(s) to undertake. To take the diagnostic test please send an email to clt@anu.edu.au or click the button below.

### More Information

Further information about the ANU First-Year Maths Bridging Modules can be found here.

### Delivery and dates

There are 3 separate Bridging Modules that will run from early January to early February 2025.

Each module will consist of two hours of lectures in the morning and a two-hour workshop in the afternoon.

* All courses will be delivered online*.

*Zoom details and password will be provided 7 days prior to commencement once enrolment is paid for and confirmed.*

**Module 1**- designed to prepare students for MATH1003*This course is offered over 8 consecutive working days***Module 2**- designed to prepare students for MATH1013*This course is offered over 9 consecutive working days***Module 3**- designed to prepare students for MATH1113 and MATH1115*This course is offered over 9 consecutive working days*

It is not recommended that students enrol in all 3 modules unless they feel they would benefit from completing Module 1 as revision.

## Structure and content

The bridging modules will run each day from 10am to 3pm. The daily schedule is as follows:

**Session 1:**10am-12pm**Break:**12pm-1pm**Session 2:**1pm-3pm

Students will also need to spend time studying outside of class time.

### Lecture Style

Each bridging module will comprise two lectures per day, each lasting 2 hours. Each lecture will proceed according to the following format:

- Content delivery (45 min)
- Q&A session (15 minutes)
- Interactive Problem Solving (45 min)
- Quiz (15 min)

### Bridging modules

## Bridging Module 1: early January 2024 (8 consecutive working days)

Bridging Module 1: early January 2024 *(8 consecutive working days)*

- Basic set theory: definition of a set, intersection, union, complement. [One lecture]
- Real numbers, inequalities, distance between two points, absolute value. [One lecture]
- Equation of a straight line (slope formula, point-slope equation, slope-intercept), parallel lines, perpendicular lines. [One lecture]
- Polynomials, long division, factoring polynomials, completing the square, finding roots.[One lecture]
- How to solve an equation (factoring, completing the square, quadratic formula). [One lecture]
- Complex numbers: imaginary unit, sum, difference, multiplication, conjugate, reciprocal, quotient of two complex numbers, quadratic equations. [One lecture]
- How to solve inequalities: interval notation, properties, combined inequalities, inequality involving absolute value. [One lecture]
- Functions and their graphs: domain,composite functions, even and odd functions, minima and maxima, piecewise defined functions, vertical and horizontal shifts, streches and compressions, reflection. [One lecture]
- Rational functions: properties, domain of a rational function, graphs, asymptotes. [One lecture]
- Exponential and logarithm functions. [Two lectures]
- Trigonometric functions and trigonometric identities. [Two lectures]
- Polar coordinates, polar equations and graphs, converting from rectangular to polar and from polar to rectangular. [One lecture]
- Vectors: direction and magnitude, position vector, addition and subtraction, unit vector, dot prduct, cross product. [One lecture]
- Binomial Theorem. Counting and probability: counting formula, permutations and combinations, compound probabilities. [Two lectures]
- Basic calculus: finding limits, one-sided limits, continuous functions. [One lecture]
- Basic calculus: Derivative of a function: product, quotient, chain rule. [One lecture]
- Basic calculus: Anti-differentiation, definite integral, area under a curve. [One lecture]

## Bridging Module 2: mid January (9 consecutive working days)

Bridging Module 2: mid January 2024 *(9 consecutive working days)*

- Functions: Definition, Graph of a Function, Composite Functions. [One lecture]
- How to solve inequalities: interval notation, properties, combined inequalities, inequality involving absolute values. [One lecture]
- Polynomial Functions; Real and Complex Zeros. [One lecture]
- One to One Functions and Inverse Functions. [One lecture]
- Exponential and logarithm functions [One lecture]
- Exponential and Logarithmic Equations. [One lecture]
- Trigonometric Functions. [One lecture]
- Inverse Trigonometric Functions. [One lecture]
- Trigonometric Identities: Sum and Difference Formulas, Double and Half Angles
- Limits and Continuity. [One lecture]
- Limits Involving Infinity. [One lecture]
- The Tangent Problem, Definition of the Derivative. [One lecture]
- Rules for Differentiation. [One lecture]
- Derivatives of the Trigonometric Functions. [One lecture]
- Product Rule, Quotient Rule, Chain Rule. [One lecture]
- Implicit Differentiation and related rates. [One lecture]
- First and Second Derivatives; Curve Sketching. [One lecture]
- Antiderivatives. [One lecture]
- The Area Problem; the Definite Integral. [One lecture]
- Evaluating Definite Integrals: The Fundamental Theorem of Calculus. [One lecture]
- The Substitution Rule.[One lecture]
- Integration by Parts. [One lecture]
- Areas between Curves. [One lecture]

## Bridging Module 3: early February 2024 (9 consecutive working days)

Bridging Module 3: early February 2024 *(9 consecutive working days)*

- Functions and their representations. [One lecture]
- How to solve inequalities: interval notation, properties, combined inequalities, inequality involving absolute values. [One lecture]
- Precise definition of a limit. [One lecture]
- Limits and continuity. [One lecture]
- Limits involving infinity. [One lecture]
- Formal definition of derivative and rules for differentiation [One lecture]
- Implicit differentiation. [One lecture]
- Trigonometric functions and their inverse. [One lecture]
- Hyperbolic functions and their inverse. [One lecture]
- Indeterminate forms and L’Hopital’s Rule. [One lecture]
- First and second derivatives; curve sketching. [One lecture]
- Antiderivatives. [One lecture]
- The area problem; the definite integral. [One lecture]
- Evaluating definite integrals: The Fundamental Theorem of Calculus. [One lecture]
- The Substitution Rule.[One lecture]
- Integration by Parts. [One lecture]
- Trigonometric integrals and substitutions. [Two lectures]
- Partial Fractions. [Two lectures]

## How to apply

*Please note: It is mandatory that students complete the diagnostic test prior to enrolment.*

The 3 Bridging Modules will run from early January to early-February 2024.

## Fees

- Bridging Module 1: Cost: AUD $515
- Bridging Module 2: Cost: AUD $550
- Bridging Module 3: Cost: AUD $550

The cost for each module is inclusive of:

- Tuition Fees
- Academic Activities

Students who later enrol in a mathematics course at the ANU, can apply for a refund of AUD $100 per module by contacting the Bridging Course administrator at admin.teaching.msi@anu.edu.au.

The performance results of the diagnostic test will indicate whether a student should take one or two bridging modules.

It is not recommended that students enrol in all 3 Bridging Modules. If, however you are considering this option, please email james.borger@anu.edu.au with the following details:

- The mathematics course you studied in Year 12
- The mathematics course you intend to enrol in at ANU

## Cancellation

The Australian National University reserves the right to cancel the modules or change modules title, content, dates and venues. We also reserve the right to decline registrations where registrations exceed capacity or cancel the modules due to insufficient registrations. In the event of cancellation, students registered for one or more modules will be notified 14 days prior to commencement.

Registered students who wish to cancel must provide written confirmation of their intention to the Bridging module administrator at admin.teaching.msi@anu.edu.au by the following dates:

Module 1: 7 days prior to commencement

Module 2: 7 days prior to commencement

Module 3: 7 days prior to commencement

## Refunds

Under the circumstances outlined below, students may be eligible for a full refund of their fees.

- If ANU is unable to offer the course
- If a student’s visa application is refused. Evidence of refusal is mandatory and students must provide the decision record from the Department of Home Affairs in the case of a visa refusal
- If a student cancels their place in the course in writing, by the dates outlined above.

## Enrol and payment link

Please enrol here