The Guide to Mathematics of Business and Finance, 2nd Edition (Version 1.0 2024)

Abstract

This guide covers foundational topics of business and financial mathematics usually discussed in a typical one semester course offered by business schools of Canadian Colleges of Applied Arts and Technology. The guide is suitable for diploma or degree-level courses.

The following topics are discussed: Percent and percent change, compound percent, simple and compound interest, annuities and perpetuities, loan amortization and mortgages, fixed income instruments, NPV, sequences of discounts, exchange rates, invoices, price structure, break-even analysis.

The topics are explained by means of numerous examples. There are also end-of-chapter exercises with full solutions.

The second edition of the guide introduces the use of artificial intelligence technologies, specifically Wolfram|Alpha and ChatGPT 4, to solve business and financial mathematics problems. Students will benefit from such content in several ways:

• Becoming familiar with powerful systems like Wolfram|Alpha and ChatGPT. • Learning to use advanced AI technologies alongside standard tools such as calculators and Microsoft Excel. • Gaining deeper understanding of the subject matter by using AI as a source of information, interacting with AI and analyzing its responses. • Learning to receive hints from AI when facing difficulties. • Learning the art of AI prompting. • Becoming more efficient in calculations, with Wolfram|Alpha providing assistance for complex computational tasks. • Appreciating the necessity of deep subject matter knowledge in evaluating AI responses and creating clear, effective prompts. • Recognizing limitations of AI assistance. • Developing transferable skills for interacting with AI to solve problems in other knowledge areas.

The academic philosophy of the guide is based on five pillars:

1. Briefness. The focus is only on the essential information. 2. Algebraic method. The priority is given to algebraic problem solving. However, essential Artificial Intelligence, calculator and Excel techniques are also discussed in the guide. 3. Logical flow. One topic sets the foundation for another topic. Careful reading without skipping is necessary. 4. Examples. Topics are explained using many carefully selected examples. There are also end-of-chapter exercises with full solutions. 5. No memorization. If used properly, the guide must lead to the level of understanding allowing to solve problems without having to remember many formulas and without using a formula sheet.

The first edition of the guide can be found here: https://openlibrary.ecampusontario.ca/item-details/#/ff8d31a1-2c14-4831-a403-3a61a46169a0