This book contains a selection of more than 500 mathematical problems and their solutions from the PhD qualifying examination papers of more than ten famous American universities. The mathematical problems cover six aspects of graduate school mathematics: Algebra, Topology, Differential Geometry, Real Analysis, Complex Analysis and Partial Differential Equations. While the depth of knowledge involved is not beyond the contents of the textbooks for graduate students, discovering the solution of the problems requires a deep understanding of the mathematical principles plus skilled techniques. For students, this book is a valuable complement to textbooks. Whereas for lecturers teaching graduate school mathematics, it is a helpful reference.

This new and expanded edition is intended to help candidates prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Paper). STEP is an examination used by Cambridge Colleges for conditional offers in mathematics. They are also used by some other UK universities and many mathematics departments recommend that their applicants practice on the past papers even if they do not take the examination. Advanced Problems in Mathematics bridges the gap between school and university mathematics, and prepares students for an undergraduate mathematics course. The questions analysed in this book are all based on past STEP questions and each question is followed by a comment and a full solution. The comments direct the reader's attention to key points and put the question in its true mathematical context. The solutions point students to the methodology required to address advanced mathematical problems critically and independently. This book is a must read for any student wishing to apply to scientific subjects at university level and for anyone interested in advanced mathematics.

National Curriculum guidelines emphasise knowledge, understanding and skills. The author, an internationally recognised authority, provides teachers with a clear explanation of these principles, and explains the relation between understanding and skills, and describes their application to the teaching of mathematics. The book contains numerous activities to show how mathematics can be learnt in the primary classroom with understanding and enjoyment, including: * formation of mathematical concepts * construction of knowledge * contents and structure of primary mathematics

555 SAT MATH BOOK, a series of 555 Math Books, was written especially for students in a way that they would excel in Scholastic Assessment Test (SAT) Mathematics Section. The book consists of 555 Math questions and the solutions to those problems are also included. The book covers the framework of SAT, which includes concepts of Algebra I and II, Arithmetic, Probability, Data Analysis, Plane Geometry, Coordinate Geometry and Trigonometry. Of these concepts, Algebra makes up the largest part of the test, accounting more than half of the questions. Some of those questions are easy to solve even with the least knowledge of math, because all of them come with the easiest and shortest possible solution methods. Harder questions come with formulas and short tips explaining the answers.

A comprehensive overview of elementary, middle, and high-school mathematics. Intended as a supplement to any math program, this book provides additional math explanation from basic to advanced levels. Emphasis is placed on why problems are solved in a certain manner. Tailored for those who need simplified, easy-to-read additional explanations of math concepts.

New edition includes extensive revisions of the material on finite groups and Galois Theory. New problems added throughout.

Over 300 unusual problems, ranging from easy to difficult, involving equations and inequalities, Diophantine equations, number theory, quadratic equations, logarithms, more. Detailed solutions, as well as brief answers, for all problems are provided.