# Mathematical Sciences Institute

### 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. Take the test here

### More Information

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

### Maths Bridging Modules delivery and dates

There are 3 separate Bridging Modules that will run from early January to early-February 2023.

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**

**Module 1**- designed to prepare students for MATH1003 – 4-13 January 2023

* This course is offered over 8 consecutive working days*

**Module 2**- designed to prepare students for MATH1013 – 16 January - 27 January 2023

* This course is offered over 9 consecutive working days*

**Module 3**- designed to prepare students for MATH1115 – 30 January - 9 February 2023

* 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.

Wed 04 Jan 2023 - Fri 13 Jan 2023

10:00 - 15:00

8 Sessions

Online

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

**Module 1** - designed to prepare students for MATH1003

*This course is offered over 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]

Mon 16 Jan 2023 - Fri 27 Jan 2023

10:00 - 15:00

9 Sessions

Online

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

**Module 2** - designed to prepare students for MATH1013

*This course is offered over 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]

Mon 30 Jan 2023 - Thu 09 Feb 2023

10:00 - 15:00

9 Sessions

Online

**Module 3** - designed to prepare students for MATH1115

*This course is offered over 9 consecutive working days *

### 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.