TOP BOOKS TO READ IF YOU WANT TO STUDY
MATHEMATICS AT UNIVERSITY www.immerse.education
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Mathematics at school and mathematics at university are wildly different subjects.
With so much literature to choose from, which reading should a prospective student prioritise? Immerse Education is here to help. We spoke with our mentor team who are currently studying Mathematics at top universities to ask them which books they think a young student should read before applying.
Table of Content The list below is some of the titles they recommended in no particular order. Letters to a Young Mathematician �������������������������� 4 by Ian Stewart
How to Think Like a Mathematician ������������������������ 5 by Kevin Houston
Calculus ������������������������������������������������������������������ 6 by Michael Spivak
How Not to Be Wrong: The Hidden Maths of Everyday Life ������������������������������������������� 7 by Jordan Ellenberg
What is Mathematics: An Elementary Approach to Ideas and Methods ������������������������������������������������� 8 by Herbert Robbins and Richard Courant
Symmetry and the Monster ������������������������������������� 9 by M. Ronan
Letters to a Young Mathematician by IAN STEWART
'Letters to a Young Mathematician' provides valuable insight into the journey from high school student to university undergraduate.
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t is an excellent informal introduction to studying a maths degree, including sections on the differences between maths at school and university, proofs and formal logic, and how to integrate into the mathematical community.
Ian Stewart wrote ‘Letters to a Young Mathematician’ having in mind the things he wishes he had known when he was a student. From the philosophical to the practical, Stewart asks what mathematics is and why it’s worth doing! Two very important questions for a prospective student. He considers the relationship between logic and proof, the role of beauty in mathematical thinking, and finally, the future of mathematics. Stewart has an easygoing humour which makes him an enjoyable and accessible read. It is certainly a book that will make you more excited to be studying maths at university.
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How to Think Like a Mathematician by KEVIN HOUSTON
‘How To Think Like A Mathematician’ is a great introduction to studying undergraduate mathematics.
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his book gives advice on how to approach mathematical problems and the thought processes one should use, as well as tips on how to read and write mathematics. Prospective students can learn many new things from this book, things which will be used on a daily basis during an undergraduate maths degree. This book does an excellent job of bridging the gap between school and university mathematics, not least because the book is designed precisely for this. The reader is first introduced to the rudimentary objects that underpin mathematics (sets, functions, and so on) and then gradually taught the fundamentals of mathematical thinking. By the end of the book, not only is the reader familiar with the basics of real mathematics, but an appreciation of the true nature of mathematics and of mathematical rigour is gained.
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Calculus by MICHAEL SPIVAK
‘Calculus’ is an outstanding book for prospective applicants to see what mathematical rigour entails in practice.
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alculus is an outstanding book for prospective applicants to see what mathematical rigour entails in practice, when applied to a branch of mathematics they are most likely already familiar with: calculus.
It is a fascinating read, beginning right from the basics of sets and functions before developing the notions of differentiation and integration and moving onto sequences and series. That basic results in calculus known from school are proven rigorously is especially enlightening in terms of instilling in the reader an understanding of what real, rigorous mathematics is like.
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How Not to Be Wrong: The Hidden Maths of Everyday Life by JORDAN ELLENBERG
‘How Not To Be Wrong’ is an excellent book about the application of maths to the real world and surprising results of statistics.
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he maths we learn in school can seem like an abstract set of rules, laid down by the ancients and not to be questioned. What Jordan Ellenberg seeks to shows us is that maths touches on everything we do, and a little mathematical knowledge reveals the hidden structures that lie beneath the world’s messy and chaotic surface. In ‘How Not to be Wrong’, Ellenberg explores the mathematician’s method of analyzing life, from the everyday to the cosmic, showing us which numbers to defend, which ones to ignore, and when to change the equation entirely. Along the way, he explains calculus in a single page, describes Gödel’s theorem using only one-syllable words, and reveals how early you actually need to get to the airport.
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What is Mathematics: An Elementary Approach to Ideas and Methods by HERBERT ROBBINS AND RICHARD COURANT
‘What is Mathematics’ covers a diverse range of mathematical topics and seeks to explain them from the ground up.
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ritten for beginners and scholars, for students and teachers, for philosophers and engineers, ‘What is Mathematics?’ is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics. Each chapter covers a distinct field and is largely independent, making it possible for the reader to easily target topics of interest. Although the emphasis of this book is on pure mathematics, it could be recommended to anyone wanting to pursue a degree in Physics as it equips you with the mathematical fluency necessary for a Physics course.
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Symmetry and the Monster
Symmetry underpins expansive areas of science.
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rom conservation laws, to molecular symmetry, to vector spaces, the appreciation of this bridge between the abstract mathematics of Group Theory and its implications in the physical sciences lays bare the foundations of many of the concepts found in the first year of undergraduate study in the sciences, often taken for granted by a young scientist. Ronan aims more for conceptual understanding; this is not a book on mathematics filled with equations. It is an interesting and informative essay on a concept that will rationalise the study of every science student.
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