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An Introduction to Pre-University Mathematics

James Ward and Siri Kouletsis

This course introduces some of the basic ideas and methods of mathematics with an emphasis on their application.

It works at an elementary level with the aim of developing sophisticated mathematical skills and bridging the gap between school leavers and undergraduate study.

At the end of the mathematics course, you should be able to:

Manipulate and use algebraic expressions
Graph, differentiate and integrate simple functions
Calculate basis quantities in financial mathematics

What you'll learn

This course will provide you with:

A grounding in arithmetic and algebra
An overview of functions and the fundamentals of calculus
An introduction to financial mathematics

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What's inside

Syllabus

Arithmetic and Algebra

A review of arithmetic and the manipulation of algebraic expressions (including the use of brackets and power laws).

Solving linear equations and the relationship between linear expressions and straight lines.

Solving quadratic equations

The relationship between quadratic expressions and parabolae.

Functions

An introduction to functions such as polynomials, exponentials, logarithms, and trigonometric functions.

The existence of inverse functions and how to find them.

The laws of logarithms and their uses.

Calculus

The meaning of the derivative and how to find it (including the product, quotient, and chain rules).

Using derivatives to find approximations and solve simple optimisation problems with economic applications.

Curve sketching

Integration of simple functions and using integrals to find areas.

Financial mathematics

Compound interest over different compounding intervals.

Arithmetic and geometric sequences.

Investment schemes

Assessing the value of an investment

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Develops skills and knowledge that have strong cross-discipline relevance and applications

Provides a strong foundation to learners new to this topic

Is taught by James Ward and Siri Kouletsis, who teach in the Computer Science department at The University of Melbourne, which is recognized for the quality of its computer science faculty

Does not explicitly require students to come in with extensive background knowledge, making it a more accessible introductory course

Teaches skills, knowledge, and tools that are highly relevant in academic settings

Covers topics at an elementary level, making it accessible to learners of all experience levels

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Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in An Introduction to Pre-University Mathematics with these activities:

Review the basic concepts of algebra and trigonometry

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Ensures that students have a strong foundation in the prerequisite mathematical concepts necessary for success in the course.

Browse courses on Algebra

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Review your notes from previous algebra and trigonometry courses
Take practice problems to test your understanding
Seek help from a tutor or online resources if needed

Follow the MIT OpenCourseWare tutorial on 'Mathematics for Computer Science'

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Introduces the fundamental mathematical concepts used in computer science and provides a solid foundation for the course.

Browse courses on Mathematics

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Watch the video lectures
Complete the practice problems
Participate in the online discussion forum

Create a concept map of the different mathematical topics covered in the course

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Provides a visual representation of the course content and helps students understand the interconnections between different topics.

Browse courses on Mathematics

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List the main mathematical topics covered in the course
Identify the relationships between the topics
Create a visual representation of the concept map

Five other activities

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Review 'Algebra: A Graduate Course' by I.N. Herstein

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Provides a comprehensive review of abstract algebra and prepares the student to succeed in the course by building a strong knowledge base in the field of algebra.

View Topics in Algebra on Amazon

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Read the chapters on basic algebraic structures
Focus on understanding group theory and field theory
Solve the exercises at the end of each chapter

Solve problems from the 'Mathematics for Economists' textbook by Simon and Blume

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Provides practice in applying mathematical concepts to economic problems and strengthens problem-solving skills.

View Exam Prep for Mathematics for Economists by... on Amazon

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Choose a section of the textbook
Solve the odd-numbered problems
Check your answers against the solutions manual

Join a study group with other students taking the course

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Provides a supportive and collaborative environment for learning and problem-solving.

Browse courses on Mathematics

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Find other students who are interested in forming a study group
Set up a regular meeting time and location
Work together on homework problems and review course material

Attend the 'Mathematics and its Applications' conference

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Provides an opportunity to connect with other students and professionals in the field of mathematics and learn about the latest research and applications.

Browse courses on Mathematics

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Register for the conference
Attend the keynote speeches
Participate in the breakout sessions

Develop a mathematical model to solve a real-world problem

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Applies mathematical principles to a practical problem and enhances problem-solving and critical thinking skills.

Browse courses on Mathematics

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Define the problem and identify the relevant variables
Develop a mathematical model that represents the problem
Solve the model and analyze the results
Present the findings and discuss the implications

Career center

Learners who complete An Introduction to Pre-University Mathematics will develop knowledge and skills that may be useful to these careers:

Risk Manager

Risk managers identify, assess, and manage risks for businesses and organizations. This course provides a strong foundation in financial mathematics, which is essential for success in this role.

See salaries and explore the career path for Risk Manager

Financial Analyst

Financial analysts provide advice to businesses and individuals on investment and financial planning. This course provides a strong foundation in financial mathematics, which is essential for success in this role.

See salaries and explore the career path for Financial Analyst

Quantitative Analyst

Quantitative analysts use mathematical and statistical methods to analyze financial data and develop trading strategies. This course provides a strong foundation in financial mathematics, which is essential for success in this role.

See salaries and explore the career path for Quantitative Analyst

Investment Banker

Investment bankers help businesses raise capital and advise them on mergers and acquisitions. This course provides a strong foundation in financial mathematics, which is essential for success in this role.

See salaries and explore the career path for Investment Banker

Financial Planner

Financial planners provide advice to individuals and families on investment and financial planning. This course provides a strong foundation in financial mathematics, which is essential for success in this role.

See salaries and explore the career path for Financial Planner

Operations Research Analyst

Operations research analysts use mathematical and statistical methods to improve the efficiency of businesses and organizations. This course provides a strong foundation in algebra and calculus, which are essential for success in this role.

See salaries and explore the career path for Operations Research Analyst

Statistician

Statisticians collect, analyze, and interpret data to help businesses and organizations make informed decisions. This course provides a strong foundation in algebra and calculus, which are essential for success in this role.

See salaries and explore the career path for Statistician

Data Analyst

Data analysts collect, clean, and analyze data to help businesses make informed decisions. This course provides a strong foundation in algebra and calculus, which are essential for success in this role.

See salaries and explore the career path for Data Analyst

Actuary

Actuaries use mathematical and statistical methods to assess risk in insurance, finance, and other industries. This course provides an introduction to the fundamentals of calculus, which is essential for success in this role.

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Teacher

Teachers help students learn and develop their critical thinking skills. This course provides a strong foundation in algebra and calculus, which are essential for success in this role.

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Credit Analyst

Credit analysts assess the creditworthiness of individuals and businesses. This course provides a strong foundation in financial mathematics, which is essential for success in this role.

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Auditor

Auditors examine financial records and ensure that they are accurate and in compliance with the law. This course provides a strong foundation in financial mathematics, which is essential for success in this role.

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Accountant

Accountants prepare and examine financial records to ensure that they are accurate and in compliance with the law. They also offer advice on financial matters. This course provides a strong foundation in financial mathematics, which is essential for success in this role.

See salaries and explore the career path for Accountant

Budget Analyst

Budget analysts help businesses and organizations create and manage their budgets. This course provides a strong foundation in financial mathematics, which is essential for success in this role.

See salaries and explore the career path for Budget Analyst

Management Consultant

Management consultants provide advice to businesses on strategy, operations, and financial planning. This course provides a strong foundation in algebra and calculus, which are essential for success in this role.

See salaries and explore the career path for Management Consultant

Reading list

We've selected 12 books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in An Introduction to Pre-University Mathematics.

Linear Algebra and Its Applications

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A classic textbook on linear algebra, providing a comprehensive overview of the subject.

An Introduction to Pre-University Mathematics

What you'll learn

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What's inside

Syllabus

Good to know

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Activities

Career center

Reading list

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