Foundational Mathematics for Actuaries / CFA / FRM from Udemy

Course Overview

Before writing the Actuarial, CFA or FRM Exams, you need to have a solid understanding of Mathematics. In this course we will go through the International Actuarial Association syllabus requirements for Foundational Maths which is very similar to the requirement for CFA and FRM. We will look at Set Theory, Functions, Differentiation and Integration. Once you have completed this course you will be able to attempt the Mathematical Statistics and Financial Mathematics exams of the Actuarial Profession.

Contents

Sets and Function
1. Set Theory
2. Functions
Differentiation
1. Rules of Differentiation
2. Finding Stationary Points on a curve
3. Chain Rule
4. Product & Quotient Rule
5. Partial Derivatives
6. Finding Stationary Points on a surface
7. Lagrange Multipliers for Optimal Solutions
Integration
1. Introduction to the Integral
2. Integration by Inspection
3. Partial Fractions
4. Integration by Substitution
5. Integration by Parts
6. Double Integrals
Differential Equations
1. General Solution
2. Particular Solution
3. Two Functions
4. Integrating Factors
Sequences & Series
1. Introduction to Sequences and Series
2. Theory of Sequences
3. Arithmetic Progression
4. Geometric Progression
5. Series
Linear Algebra
1. Introduction to Linear Algebra
2. Vectors and their Operations
3. Matrices and their Operations
4. Determinants and Inverse Matrices

About the Presenter:

Hi I'm MJ the Fellow Actuary. I've been making educational videos since 2013 on YouTube. I've passed all the actuarial exams and am here to help you do the same. I've majored in Mathematical Statistics and have published research in the South African Journal of Science on Artificial Intelligence. I've also done a Ted Talk on advanced studying methods. As your instructor my purpose is to make sure you understand every concept in these courses. If you get stuck with anything, send me a message, I'm here to help.

Other Courses that I offer:

Introduction to R programming
Mathematical Statistics
Financial Mathematics
And more on Actuarial Science and Finance

What's inside

Learning objectives

Set theory
Functions and terminology
Differentiation
Chain rule, product rule & quotient rule
Stationary points for univariate and bivariate functions
Lagrange multipliers for constrained problems
Integration
Technique 1: integration by inspection
Technique 2: partial fractions

Technique 3: integration by substitution
Technique 4: integration by parts
Double integrals
Differential equations
Sequences and series
Linear algebra
Show more
Show less

Set theory
Functions and terminology
Differentiation
Chain rule, product rule & quotient rule
Stationary points for univariate and bivariate functions
Lagrange multipliers for constrained problems
Integration
Technique 1: integration by inspection
Technique 2: partial fractions
Technique 3: integration by substitution
Technique 4: integration by parts
Double integrals
Differential equations
Sequences and series
Linear algebra
Show more
Show less

Syllabus

Introduction

In this video we introduce the foundational mathematical topics you need to become a financial professional. While I am an Actuary and the video is designed for an actuarial audience, the same topics are required for the CFA and FRM profession. Most actuaries specialise in Life Insurance whereas I specialised in Enterprise Risk Management and Financial Applications. Enterprise Risk Management is very similar to FRM and Financial Applications is very similar to CFA.

Set Theory is the foundation of Mathematics

Definition
Subset
Union
Intersection
Range Notation
Important Sets
Complements

At a High School reunion everyone discussed the games they used to play:

50 played pokemon

50 played chess

40 played Fortnite.

15 played both pokemon and chess,

20 played both chess and Fortnite

15 played both pokemon and Fortnite

10 played all three.

Everyone played at least 1 game.

Answer the following multiple choice questions

Traffic lights

Read about what's good

what should give you pause

and possible dealbreakers

Covers foundational mathematics, which is essential for quantitative finance roles and actuarial science, providing a strong base for further studies

Includes topics like set theory, differentiation, and integration, which are fundamental concepts tested in actuarial, CFA, and FRM exams

Explores linear algebra, which is crucial for understanding portfolio optimization and risk management in finance and actuarial contexts

Features sequences and series, which are important for understanding time value of money and financial modeling in actuarial science and finance

Requires a solid understanding of mathematics before attempting the Actuarial, CFA, or FRM exams, suggesting it is best suited for beginners

Taught by a Fellow Actuary with experience in Enterprise Risk Management, which is similar to FRM, and Financial Applications, which is similar to CFA

Reviews summary

Foundational math for actuarial, cfa, frm exams

According to students, this course provides a solid foundation for the mathematical concepts needed for the Actuarial, CFA, and FRM exams. Many learners found the explanations to be clear and concise, particularly praising the instructor, MJ, for his ability to explain complex topics simply. The course is described as well-structured and a good starting point, though some note it might be too basic for those with stronger math backgrounds. Reviewers frequently mention the course's coverage of calculus (differentiation and integration), linear algebra, and other core areas as very helpful for exam preparation. While it covers foundational material well, some students suggest it may require additional practice or supplementary resources for complete exam readiness.

Offers a good start, but may be basic for some.

"Excellent course to review the core concepts that are foundational."

"Very helpful for someone who needs to brush up on their math skills before diving into financial applications."

"If you have a strong math background, this course might feel too much like a review."

"While it covers the basics well, advanced learners might find it moves too slowly through certain topics."

Covers wide range of foundational math topics.

"I liked that it covered Set Theory, Calculus, Differential Equations, and Linear Algebra – everything needed."

"The sections on integration and differentiation were particularly well done and useful."

"It provides a good overview of all the necessary foundational math areas listed in the syllabus."

"The linear algebra part was a good introduction to the topic for these exams."

Helpful foundation for finance/actuarial exams.

"This course is an excellent starting point for anyone preparing for the Actuarial, CFA, or FRM exams."

"It covers the core mathematical topics required for these certifications thoroughly."

"I feel much more confident tackling quantitative sections on the CFA exam after reviewing this material."

"Provides a solid mathematical foundation that is essential for the subsequent actuarial exams."

Instructor explains complex concepts clearly.

"MJ explains the foundational concepts very clearly and concisely. This course helped me to revisit the concepts I had forgotten from my high school."

"The instructor explained every detail clearly and made it easy to understand, even difficult topics."

"I found the explanations of differentiation and integration particularly easy to follow."

"I really appreciated how simple the complex topics were made; it boosted my confidence."

May require more practice beyond course.

"The lectures are clear, but I needed to find external practice problems to truly solidify my understanding for the exams."

"While the theory is covered, the course could benefit from more examples and practice exercises."

"It gives you the concepts, but you need to supplement with exam-style questions."

"I felt I needed more hands-on practice with applying the concepts to exam problems."

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 Foundational Mathematics for Actuaries / CFA / FRM with these activities:

Review Precalculus Concepts

Show steps

Reinforce foundational precalculus concepts to better understand the set theory and functions sections of the course.

Browse courses on Precalculus

Show steps

Review notes and examples from precalculus courses.
Work through practice problems focusing on functions and graphing.
Identify areas of weakness and seek out additional resources.

Review 'Calculus' by James Stewart

Show steps

Supplement the course material with a comprehensive calculus textbook to deepen understanding of differentiation and integration.

View Biocalculus: Calculus, Probability, and... on Amazon

Show steps

Obtain a copy of 'Calculus' by James Stewart.
Read the chapters related to differentiation and integration.
Work through the examples and practice problems in the book.

Practice Differentiation and Integration Problems

Show steps

Sharpen differentiation and integration skills through repetitive practice problems to improve speed and accuracy.

Show steps

Find online resources or textbooks with differentiation and integration problems.
Solve a variety of problems, starting with simpler ones and gradually increasing difficulty.
Check answers and review solutions to understand mistakes.

Four other activities

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Show all seven activities

Create a Cheat Sheet for Differentiation and Integration Rules

Show steps

Consolidate understanding of differentiation and integration rules by creating a concise and organized cheat sheet.

Show steps

Review all the differentiation and integration rules covered in the course.
Organize the rules into a logical format, such as by type of function.
Create a visually appealing and easy-to-read cheat sheet.

Review 'Linear Algebra and Its Applications' by Gilbert Strang

Show steps

Deepen understanding of linear algebra concepts with a comprehensive textbook that provides additional examples and applications.

View Linear Algebra for Everyone on Amazon

Show steps

Obtain a copy of 'Linear Algebra and Its Applications' by Gilbert Strang.
Read the chapters related to vectors, matrices, and determinants.
Work through the examples and practice problems in the book.

Develop a Financial Model Using Differential Equations

Show steps

Apply knowledge of differential equations to build a practical financial model, such as predicting stock prices or modeling economic growth.

Show steps

Choose a financial phenomenon to model using differential equations.
Research the relevant equations and parameters for the model.
Implement the model using software like Excel or Python.
Analyze the results and draw conclusions about the financial phenomenon.

Tutor Other Students in Foundational Mathematics

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Reinforce your understanding of the course material by explaining concepts and solving problems for other students.

Show steps

Offer tutoring services to other students in the course.
Prepare explanations and examples for common problem areas.
Provide constructive feedback and guidance to tutees.

Career center

Learners who complete Foundational Mathematics for Actuaries / CFA / FRM will develop knowledge and skills that may be useful to these careers:

Actuary

The role of an Actuary involves assessing and managing financial risks, particularly within insurance and finance. This course directly aligns with the foundational mathematical knowledge required for actuarial exams. The syllabus covers set theory, differentiation, integration, linear algebra, sequences, and series, which are all essential for actuarial modeling and problem solving. Moreover, this course is taught by a Fellow the Actuary who has passed all the exams. Learners preparing for actuarial exams should take this course.

See salaries and explore the career path for Actuary

Quantitative Analyst

Quantitative Analysts, or Quants, use mathematical and statistical methods to develop and implement trading strategies and risk management models. To succeed as a Quant, one requires a robust grasp of mathematical concepts like those covered in this course. The course covers differentiation, integration, and linear algebra. Moreover, the course's instruction on differential equations is particularly relevant for modeling dynamic systems in finance. Quants should take this course.

See salaries and explore the career path for Quantitative Analyst

Financial Analyst

A Financial Analyst typically analyzes financial data, provides forecasts, and makes investment recommendations. This course helps build a strong mathematical foundation that is useful for financial modeling and analysis. By covering topics like differentiation, integration, and linear algebra, the course provides the quantitative skills necessary to understand and apply complex financial concepts. Financial analysts will find the sections on sequences and series, as well as functions, particularly useful. Because the instructor is a Fellow Actuary with experience in finance, this course helps prepare learners for success.

See salaries and explore the career path for Financial Analyst

Risk Manager

Risk Management professionals identify and mitigate potential risks for organizations. This course provides the mathematical tools necessary to quantify and model risk. The coverage of set theory helps in understanding event probabilities, while differentiation and integration are essential for creating risk models. The course's examination of linear algebra can be useful when working with portfolios of financial assets. Since the instructor is an actuary with experience in enterprise risk management, this course provides targeted training.

See salaries and explore the career path for Risk Manager

Statistician

Statisticians collect, analyze, and interpret data to draw conclusions and make informed decisions. A strong mathematical foundation is crucial for understanding statistical methods and developing new ones. This course covers essential topics such as set theory, differentiation, integration, and linear algebra. By studying through this course, Statisticians can improve their abilities in the workplace.

See salaries and explore the career path for Statistician

Economist

Economists study the production, distribution, and consumption of goods and services. This course provides the mathematical tools used in economic modeling and analysis. Differentiation and integration are used extensively in optimization problems, while linear algebra is used to model systems of equations. Anyone considering a career as an Economist should take this course.

See salaries and explore the career path for Economist

Data Scientist

Data Scientists analyze large datasets to extract meaningful insights and develop predictive models. This course can be useful because it provides the mathematical building blocks for many data science techniques. Linear algebra is fundamental to machine learning algorithms, while calculus (differentiation and integration) is used in optimization problems. Data Scientists benefit through solidifying their understanding of sequences and series, helping them to get ahead in their roles.

See salaries and explore the career path for Data Scientist

Budget Analyst

Budget Analysts help organizations plan and manage their finances by preparing budgets, analyzing financial data, and making recommendations for cost control. The course covers functions, differentiation, integration, and linear algebra. These mathematical concepts help build the basis for success as a Budget Analyst. They will find topics such as sequences and series particularly relevant.

See salaries and explore the career path for Budget Analyst

Financial Planner

Financial Planners help individuals and families manage their finances and plan for the future. While financial planning involves more than just mathematics, understanding concepts like present value, future value, and investment returns requires a solid foundation in mathematics. This course's coverage of sequences and series is particularly relevant. The instructor is a seasoned professional whom financial planners can look to for guidance.

See salaries and explore the career path for Financial Planner

Management Consultant

Management Consultants advise organizations on how to improve their performance and efficiency. While a career in management consulting is not necessarily quantitative, a strong mathematical foundation helps in analyzing data, building models, and making informed recommendations. Covering topics such as functions, differentiation, and integration, the course is useful for consultants.

See salaries and explore the career path for Management Consultant

Investment Banker

Investment Banking involves raising capital for companies, advising on mergers and acquisitions, and providing other financial services. While not immediately obvious, a solid mathematical foundation helps build a deeper understanding of financial instruments and market dynamics. Investment bankers will find the coverage of functions, sequences, and series useful for valuing assets and structuring deals. This course may be useful for success in the field.

See salaries and explore the career path for Investment Banker

Business Intelligence Analyst

Business Intelligence Analysts analyze data to identify trends and insights that can help businesses make better decisions. While this role focuses on data analysis and visualization, a strong foundation in mathematics helps in understanding the underlying statistical concepts and building more sophisticated models. Business intelligence analysts will find the course useful.

See salaries and explore the career path for Business Intelligence Analyst

Market Research Analyst

Market Research Analysts study consumer behavior and market trends to advise companies on product development, marketing strategies, and pricing decisions. While this role is primarily focused on qualitative and quantitative research methods, a solid understanding of mathematics is beneficial for analyzing survey data and building statistical models. This course may be useful for a market research analyst.

See salaries and explore the career path for Market Research Analyst

Tax Accountant

Tax Accountants prepare and file tax returns for individuals and businesses, ensuring compliance with tax laws and regulations. While tax accounting is heavily based on legal and regulatory knowledge, a solid understanding of mathematics is helpful for calculating taxes, analyzing financial data, and understanding complex tax structures. Tax accountants may find the course useful.

See salaries and explore the career path for Tax Accountant

Software Engineer

Software Engineers design, develop, and test software systems. While this role is primarily focused on coding and computer science principles, a solid understanding of mathematics is beneficial for certain areas, such as algorithm design and optimization. The course's coverage of linear algebra is particularly relevant for graphics programming and machine learning. Software engineers looking to hone their craft can take this course.

See salaries and explore the career path for Software Engineer

Reading list

We've selected two 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 Foundational Mathematics for Actuaries / CFA / FRM.

Biocalculus: Calculus, Probability, and Statistics...

Save

Provides a comprehensive overview of calculus concepts, including differentiation and integration. It widely used textbook in universities and colleges. It is particularly helpful for students who need a more in-depth explanation of the calculus topics covered in the course. It can be used as a reference text throughout the course.

Biocalculus: Calculus, Probability, and Statistics...

Loose Leaf

$$$$

Linear Algebra for Everyone

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Provides a comprehensive introduction to linear algebra, covering vectors, matrices, determinants, and inverse matrices. It popular textbook for undergraduate linear algebra courses. It is particularly helpful for students who want to deepen their understanding of the linear algebra concepts covered in the course. It provides additional examples and applications.

Linear Algebra for Everyone

Paperback

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Linear Algebra for Everyone

Kindle Edition

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Foundational Mathematics for Actuaries / CFA / FRM

What's inside

Learning objectives

Syllabus

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Reviews summary

Foundational math for actuarial, cfa, frm exams

Activities

Career center

Reading list

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