This book presents a unique interactive style that enables students to diagnose their strengths and weaknesses and focus their efforts where needed. It is ideal for self-study and tutorial work, building from an initially supportive approach to the development of independent learning skills. It includes a free website which contains solutions to all exercises, additional topics and applications, guide to learning mathematics, and practice material. Students today enter engineering courses with a wide range of mathematical skills, due to the many different pre-university qualifications studied. Bill Cox's aim is for students to gain a thorough understanding of the maths they are studying, by first strengthening their background in the essentials of each topic. His approach allows a unique self-paced study style, in which students review their strengths and weaknesses through self-administered diagnostic tests, then focus on revision where they need it, to finally reinforce the skills required.The book is structured around a highly successful 'transition' maths course at Aston University which has demonstrated a clear improvement in students' achievement in mathematics, and has been commended by QAA Subject Review and engineering accreditation reports. It is a core undergraduate text with a unique interactive style that enables students to diagnose their strengths and weaknesses and focus their efforts where needed.