Almost a year ago, I bought Mr. Bob Miller’s Calc for the Clueless series for a younger cousin (I, II, and III), and she returned the book to me after finishing her Calculus class. Last week, I started reading Calc for the Clueless: Calc I and found it to be very student friendly. Most examples are easy to follow, and the book contains practical tips in solving problems. The book has also a chapter solely dedicated to worked out maxima and minima problems.
What stands out in Calc for the Clueless: Calc I is its chapter on Curve Sketching. The author has detailed the methods of basic curve sketching and explained clearly the roles of intercepts, asymptotes, and the test for round minimums and maximums. There are a lot of step by step tutorials on sketching polynomial and rational functions.
Overall, I think Calc for the Clueless: Calc I is a good companion book for students who want to learn self study Calculus especially those who are non mathematics majors.
If you are familiar with Polya’s How to Solve It, one of the most well-known classic books in mathematical problem solving, a similar book exists for learning mathematical proofs. Daniel Velleman’s How to Prove It: A Structured Approach is one of the good books available for learning the structure of proofs.
The books include topics onm Sentential logic, Quantification Logic, Proof Strategies, Relations, Functions, Mathematical Induction and Infinite Sets. It contains detailed explanation and numerous examples on different types of proofs and the logic behind them. It contains explanations on connectives, quantifiers, truth tables, countable and uncountable sets and more.
How to Prove It is a recommended book for undergraduate mathematics students as well as advanced high school students who plan to be mathematics majors.
How to Solve Word Problems in Algebra: A Solved Problems Approach is a book ideal for middle school and high school students who want to learn about solving word problems. The book offers step-by-step method in solving different types of word problems.
The topics covered in this book are number, motion (time, rate, distance), mixtures, coins, age, lever, finance, work, digit, and problems on geometric figures. It also contains problems on quadratics and problems involving two unknowns. In addition, each chapter has worked examples and at least 10 supplementary problems with solutions.
Since the book teaches problem solving step by step, it can be a good supplementary material or self-study guide for students.
If you want to learn about word problem solving, you may also want to check Math and Multimedia’s Mathematics Word Problem Solving Series.