# Mathematical Sciences Institute

MSI aims for research and educational outcomes of the highest possible quality. This is achieved by world wide collaborative research, nurturing quality students, increasing the international profile and the efficiency of the organisation whilst ensuring administration and support functions effectively.

### 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.

### 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.

### 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.

**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]

**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]

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

*This course is offered over 9 consecutive working days *