Introduction to Modern Mathematical Computing

Jonathan M. Borwein is currently Laureate Professor in the School of Mathematical and Physical Sciences at the University of Newcastle (NSW) with adjunct appointments at Dalhousie and at Simon Fraser. He received his Doctorate from Oxford in 1974, and has published extensively in optimization, analysis and computational mathematics, and has received various prizes both for research and for exposition. He directs the University of Newcastle’s Priority Research Centre in Computer Assisted Research Mathematics and its Applications (CARMA).

From the reviews: "This book is intended to teach the reader the usage of the computer algebra system Maple. ... The book is readable and valuable to mathematics, science, and engineering undergraduates at the sophomore or above level. It could also be valuable to practitioners in those fields who want to learn Maple in situ. ... Summing Up: Recommended. Lower-division undergraduates through graduate students; professionals." (D. Z. Spicer, Choice, Vol. 49 (5), January, 2012) "This is a Maple-application book which illustrates some basic areas of mathematics by symbolic computation examples. ... The presentation is clear with all necessary details and comments for ensuring a full understanding of the considered examples. The intended beneficiaries are undergraduate students, teachers giving courses to undergraduate students, as well as programmers interested in using Maple for several classes of mathematical problems." (Octavian Pastravanu, Zentralblatt MATH, Vol. 1228, 2012) "In An Introduction to Modern Mathematical Computing with Maple, Borwein and Skerritt show that computers are an excellent companion for learning mathematics. ... The theme of the book is that Maple can supplement mathematics learning and, what is more, can do much of the mathematics for the students. ... The temptation is tremendous for students to skip the real work to have a true understanding of mathematics." (David S. Mazel, The Mathematical Association of America, June, 2012)

• -Preface. -Conventions and Notation.-1. Number Theory (Introduction to Maple, Putting it together, Enough code, already. Show me some maths!, Problems and Exercises, Further Explorations). -2. Calculus(Revision and Introduction, Univariate Calculus, Multivariate Calculus, Exercises, Further Explorations). -3. Linear Algebra (Introduction and Review, Vector Spaces, Linear Transformations, Exercises, Further Explorations). -4. Visualisation and Geometry: a postscript (Useful Visualisation Tools, Geometry and Geometric Constructions). –A. Sample Quizzes (Number Theory, Calculus, Linear Algebra). –Index. –References