Helps to ease the transition between school/college and university mathematics by (re)introducing readers to a range of topics that they will meet in the first year of a degree course in the mathematical sciences, refreshing their knowledge of basic techniques and focussing on areas that are often perceived as the most challenging.
Each chapter starts with a "Test Yourself" section so that readers can monitor their progress and readily identify areas where their understanding is incomplete.
A range of exercises, complete with full solutions, makes the book ideal for self-study. From the reviews:
"This book has been 'written by students for students'. ... the quite talkative style makes this book a pleasant 'arm chair reading' for freshmen and event teachers. ... it can be recommended as an additional source for students in their first year calculus or linear algebra course." (Jurgen Appell, zbMATH, Vol. 1271, 2013)
"The authors of Bridging the Gap to University Mathematics
, were students at a British university. ... Their book consists of 20 independent chapters ... including two on mechanics and two on differential equations. ... Induction is done well, and there is material on logic and truth tables as well as on proof by contrapositive. ... the book could be very useful to the beginning mathematics or engineering student-and even to the professor." (James M. Cargal, UMAP Journal, Vol. 31 (1), 2010)
"The book can be used also by ... undergraduate students, graduate students (in their first years), high-school teachers, even mathematics faculty (to get ideas on making their courses more accessible to students). The book covers an array of twenty topics, from simple inequalities to series, and is easy to read, which makes it ideal for self-study. ... It is an easy and entertaining read. ... a good book to have for any student taking mathematics courses, as well as for any teacher teaching mathematics courses." (Mihaela Poplicher, The Mathematical Association of America, April, 2009)
"Bridging the Gap to University Mathematics
is intended to do exactly what the title suggests. Gould and Hurst were, at the time of writing, both students and one gets the feeling that their desire is to tell prospective students what they themselves wish someone had told them before they embarked on their own mathematical journey at university...The book covers a broad range of topics...Well written and easy to read, it divides the material into twenty chapters, which are broken down into manageable chunks. Every chapter begin
Bridging the Gap to University Mathematics
Inequalities.- Trigonometry, Differentiation and Exponents.- Polar Coordinates.- Complex Numbers.- Vectors.- Matrices.- Matrices as Maps.- Separable Differential Equations.- Integrating Factors.- Mechanics.- Logic, Sets and Functions.- Proof Methods.- Probability.- Distributions.- Making Decisions.- Geometry.- Hyperbolic Trigonometry.- Motion and Curvature.- Sequences.- Series.