Larissa Fradkin

College Algebra – Learn to Love it!


22 September 2013

Table of Contents




Lecture 1. ALGEBRA: Addition, Subtraction, Multiplication and Division of Rational Numbers

1.1 Variables

1.2 Variables and operations on variables

1.3 General remarks

1.4 Glossary of terms introduced in this Lecture

1.5 Historical notes

1.6 Instructions for self-study

Lecture 2. Applications of Elementary ALGEBRA: Solving Simple Equations

2.1 Revision: Factorisation

2.2 Revision: Adding fractions

2.3 Decision Tree for Solving Simple Equations

2.4 Applications of equations

2.5 A historical note

2.6 Instructions for self-study

Lecture 3. ALGEBRA: Exponentiation, Roots and Logarithms of Real Numbers

3.1 Types of variables and operations on variables (ctd.)

3.2 Applications

3.3 Instructions for self-study


Algebra Summary

Order of Operations Summary

Quadratics Summary

Decision Tree For Solving Simple Equations





These notes are based on the lectures delivered by the author to engineering students of London South Bank University over the period of 16 years. This is a University of widening participation, with students coming from many different countries, many of them not native English speakers. Most students have limited mathematical background and limited time both to revise the basics and to study new material. A system has been developed to assure efficient learning even under these challenging restrictions. The emphasis is on systematic presentation and explanation of basic abstract concepts. The technical jargon is reduced to the bare minimum.

Nothing gives a teacher a greater satisfaction than seeing a spark of understanding in the students’ eyes and genuine pride and pleasure that follows such understanding. The author’s belief that most people are capable of succeeding in - and therefore enjoying - the kind of mathematics that is taught at Universities has been confirmed many times by these subjective signs of success as well as genuine improvement in students’ exam pass rates. Interestingly, no correlation had ever been found at the Department where the author worked between the students’ qualification on entry and graduation.

The book owns a lot to the authors’ students – too numerous to be named here - who talked to her at length about their difficulties and successes, e.g. see Appendix VII on Teaching Methodology. One former student has to be mentioned though – Richard Lunt – who put a lot of effort into making this book much more attractive than it would have been otherwise.

The author can be contacted through her website All comments are welcome and teachers can obtain there the copy of notes with answers to questions suggested in the text as well as detailed Solutions to suggested Exercises. The teachers can then discuss those with students at the time of their convenience.

Good luck everyone!


Throughout when we first introduce a new concept (a technical term or phrase) or make a conceptual point we use the bold red font. We use the bold blue to verbalise or emphasise an important idea. Two major topics are covered in this course, Elementary Algebra and Functions.

Here is a concept map of Elementary Algebra. It is best to study it before studying any of the Algebra Lectures 1 – 3 to understand where it is on the map. The more you see the big picture the faster you learn!