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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

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.

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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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Reviews summary

Comprehensive pre-university math foundation

According to learners, this course provides a solid foundation in pre-university mathematics, making complex topics understandable and well-organized. Many found it excellent for bridging the gap between school and undergraduate study, especially for STEM degrees. The explanations are clear and practice problems reinforce concepts. The inclusion of financial mathematics is often cited as a valuable and relevant bonus. However, some students noted that the pace can be fast and it may assume a certain base level of prior knowledge, potentially posing a challenge for absolute beginners or those needing extensive foundational review.

The financial mathematics module is a relevant and practical addition.

"The financial mathematics part was a nice bonus too, very relevant."

"The examples were practical, especially in the financial math section."

"The financial math part was a pleasant and relevant addition."

Instructor's style makes complex topics highly understandable.

"The explanations were incredibly clear and the practice problems reinforced the concepts perfectly."

"The instructor's teaching style is very engaging, making complex topics understandable."

"The material is well-organized and the logical progression of topics is commendable."

Provides comprehensive and well-structured mathematical grounding.

"This course was exactly what I needed to brush up on my math skills before starting university."

"A solid foundation builder for pre-university math. The content is comprehensive, covering algebra, functions, and an introduction to calculus."

"Fantastic preparatory course! It really helped me consolidate my understanding of algebra and introduced me smoothly to calculus."

"Perfect for pre-university preparation. The lectures were clear... it covers all the necessary ground."

Could benefit from more visual aids and interactive elements.

"My only feedback would be to maybe add more interactive elements or problem-solving sessions."

"The course content is good, but the presentation could be improved. Some parts felt a bit dry, and I wished for more visual aids or real-world examples to make the concepts stick."

Pace can be fast, assumes some prior knowledge, challenging for absolute beginners.

"Some topics felt a bit rushed, particularly towards the end, and I occasionally needed to consult external resources for more in-depth explanations."

"I found some of the explanations to be too high-level for a true 'introduction'. If you're coming in with very limited prior math, you might struggle. It assumes a certain base level."

"I struggled with this course. Despite the 'introduction' title, it felt like it jumped straight into advanced concepts without enough foundational review."

"It might be better for those who just need a refresher, not a complete learning experience."

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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Show all eight activities

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:

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.

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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

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.

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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.

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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

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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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.

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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.

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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.

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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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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.

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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.

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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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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

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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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

What's inside

Syllabus

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Save this course

Reviews summary

Comprehensive pre-university math foundation

Activities

Career center

Reading list

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