Hey, math people! The University of Cambridge prepared a unique list of math books you should read in 2022.
This list of interesting math books you should read is mainly intended for sixth-formers planning to take a degree in mathematics. However, everyone who likes mathematics should look at some very suitable items for less experienced readers, and even the most hardened mathematician will probably find something new here.
What are the most useful math books you should read?
The range of mathematics books now available is enormous. This list contains a few suggestions that you should find helpful. They are divided into three groups: historical and general which aim to give a broad idea of the scope and development of the subject; recreational, from problem books which aim to keep your brain working, to technical books, which give you insight into a specific area of mathematics and include mathematical discussion; and textbooks which cover a topic in advanced mathematics of the kind that you will encounter in your first year at university.
A survey to determine the mathematical theorem with the most aesthetic appeal was conducted in 1988 by the quarterly publication The Mathematical Intelligencer. Readers were asked to give each of the twenty-four theorems a “score for beauty.” Even though there were many deserving rivals, “Euler’s equation” emerged victorious. In a similar survey of the “greatest equations” conducted by Physics World in 2004, it was discovered that Euler’s mathematical solution was second only to Maxwell’s equations among scientists. Euler’s equation “reaches down into the very depths of existence,” as Stanford mathematician Keith Devlin put it, “like a Shakespearian sonnet that catches the very essence of love, or a painting that brings out the beauty of the human form that is far more than simply skin deep.” What distinguishes Euler’s epi + 1 = 0 identity from other identities? In Euler’s Pioneering Equation, Robin Wilson demonstrates how this straightforward, beautiful, and profound formula connects to possibly the five most significant numbers in mathematics, each of which is connected to a unique narrative: the concept of zero, a significant mathematical advancement that opened up the idea of negative numbers; pi, an irrational number that serves as the foundation for measuring circles; the exponential e, related to exponential growth and logarithms; and the imaginary number I the square root of -1, which serves as the foundation of complex numbers. The number 1 serves as the foundation for our counting system. After a chapter on each of the components, Robin Wilson goes over how the stunning connection between them was discovered, including the numerous near-misses that prevented the formula from being discovered.
While many may associate The Simpsons with humor and satire, there is a lesser-known side to the show: mathematics. In his book, The Simpsons and Their Mathematical Secrets, Simon Singh delves into the numerous references to number theory and other mathematical concepts scattered throughout the show and its sister program, Futurama.
From Fermat’s Last Theorem to the Fibonacci sequence, viewers are unconsciously fed mathematical morsels that could form the basis of an entire university course. With interviews with the show’s writers and plenty of images and facsimiles, Singh provides a fascinating new insight into the world of The Simpsons and their hidden mathematical secrets.
“Numerous students enroll in universities each year to study mathematics (single honors or combined with another subject). Even the brightest of these students, who make up the majority of this class, will eventually find it difficult to adjust to the rigors of advanced mathematics. Some people find it challenging to switch to independent study and lecture-based learning. Mathematics goes from being primarily about calculation to being primarily about proof. Thus students are expected to engage with it differently. These modifications need not be strange; research on mathematics education has provided numerous insights into the essential corrections; nonetheless, they are not immediately apparent and do require explanation.
This book converts these evidence-based findings into straightforward counsel for a student audience. It covers every facet of pursuing a degree in mathematics, from the most intangible cerebral difficulties to the regular interactions with professors and efficient use of study time. To build a solid understanding of college mathematics, students will need to adapt and enhance their current skills, which are discussed in detail in Part 1, along with the topic of advanced mathematical reasoning. Study techniques are discussed in Part 2 in relation to the requirements for a mathematics degree. It offers realistic suggestions on how to study for exams and learn from lectures while still making time for a rewarding overall university experience.
This approachable, useful text—the first subject-specific student guide—will be required reading for everyone majoring in mathematics at a university.”
“The second edition of A Concise Introduction to Pure Mathematics, which expands on fundamental concepts in ways that will pique the interest of first-year students in mathematics and related fields and encourage further study, acts as a solid transitional text between high school and university mathematics. This textbook, which is broken up into 22 brief chapters, provides a variety of tasks, from simple math questions to more difficult ones.
Actual and complex numbers are discussed, and the author demonstrates how to use these ideas to address issues in the real world. He provides an introduction to concepts in number theory, geometry, analysis, and combinatorics.
What’s New in the Second Edition: Added information on prime numbers, which serve as the foundation for data encryption.
Examines “Secret Codes,” one of modern mathematics’ most amazing applications.
Discusses The significance of permutations in many discrete mathematics areas
The book’s capacity to be separated into four reasonably independent sections—an introduction to number systems and analysis; theory of the integers; an introduction to discrete mathematics; and functions, relations, and countability—allows for the building of courses with a variety of points of concentration.”
This highly regarded undergraduate textbook’s third edition is appropriate for teaching all of the mathematics for a course in any of the physical sciences. It includes more than 800 exercises, clear explanations of all the topics, and several worked examples. New stand-alone chapters introduce quantum operators, cover a wider range of real-world uses for complex variables, and describe the “special functions” of physical research. There are now more tabulations that are pertinent to statistics and numerical integration. This edition includes complete solutions for half the exercises in a separate manual accessible to both students and their teachers.
“This well-known and highly recommended textbook gives undergraduate engineers, physicists, chemists, and management scientists a fundamental foundation in mathematical concepts. The course content is designed with only a basic understanding of pre-university mathematics and is appropriate for the first two years of a standard University or Polytechnic program. There are numerous worked examples throughout the text, and at the end of each chapter, there is a list of unsolved problems.”
London. 23 cm. 241 pages. Illustration-filled editorial encyclopedia on plain tapa. Idiom in English. “The inside tale of the gravitational wave detection at ligo” — the cover. Includes an index and bibliographical references. Issued online as well. ISBN for the ebook version is 9781446485095. This book is second-hand and may include the marks and seals of its previous owner.
“Without assuming a prior knowledge of calculus or physics, this book gives the reader a basic introduction to chaos and fractals that is appropriate for students with a background in simple algebra. The main characteristics of chaos are introduced through straightforward iterated functions, including aperiodicity, sensitive dependency on beginning circumstances, and bifurcations. The concept of fractals is introduced as self-similar geometric objects, and the dimensions of self-similarity and box-counting are used to examine them. In the chapters that follow, Julia Sets and the Mandelbrot Set are explored. Power laws are briefly discussed first. The book’s final section explores cellular automata, unusual attractors, chaotic differential equations, and two-dimensional dynamical systems.
Over 200 end-of-chapter tasks are included, and the book is lavishly illustrated. It is a wonderful option for introductory courses in chaos and fractals because of its adaptable framework and concise, straightforward writing.”
For years, this book has been silently sitting on my shelf, intimidating me with its complex subject matter. Little did I know, James Gleick’s “Chaos: Making a New Science” would turn out to be a surprisingly engaging and enlightening read. In this book, Gleick not only explains the principles behind chaos theory, but also dives into the captivating history of this groundbreaking science.
You’ve probably heard of the “butterfly effect” – the idea that a simple flap of a butterfly’s wings can have far-reaching consequences, like triggering a tropical storm on the other side of the world. Gleick starts the book with this concept, showcasing how even minor changes in everyday processes can lead to unpredictable and wildly different outcomes.
But “Chaos: Making a New Science” goes beyond that. It delves into the fascinating world of fractals, where a seemingly simple formula can generate infinite complexity. The famous “Mandelbrot Set” is a prime example of this, with its intricate and ever-changing visuals that captivate our imagination.
The book not only challenges our perception of chaos, but also delves into the mathematical underpinnings that can replicate seemingly chaotic behavior. It explores how this way of thinking applies to various fields of science, despite initial skepticism from practitioners. It’s not just a book about technicalities, but also a tale of the politics and unconventional individuals who dared to explore uncharted territories.
Although categorized as a “science” book, “Chaos: Making a New Science” is far from dry and technical. It seamlessly weaves together narratives, diagrams, and intriguing diversions to captivate its readers. In fact, the book boasts a stunning set of color plates in its center, showcasing the breathtaking beauty of the “Mandelbrot Set.” In these mesmerizing images, we witness how chaos and mathematics can intertwine with pure artistic beauty.
Even after more than 40 years since its publication, “Chaos: Making a New Science” remains a classic and essential introduction to a science that is still relevant today. The study of chaos continues to impact various fields, from predicting weather patterns and turbulence to unraveling the mysteries of stock markets. It lays the foundation for much of our modern world, including the telecommunications network that we heavily rely on.
Don’t let the daunting nature of the topic deter you. “Chaos: Making a New Science” is an amazing and thought-provoking read, with only a few sections that may require some extra mental effort. Overall, it’s an enjoyable and enlightening journey that sheds light on a new and mysterious way of viewing the world.
“A set of issues and puzzles involving coincidence, chance, time, and fractals”
