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About the How the Other Half Thinks Reading Passage
This passage is the preface to How the Other Half Thinks: Adventures in Mathematical Reasoning by Sherman Stein. It argues that advanced mathematical ideas can be understood by anyone using only basic arithmetic and logic. The author explains why he wrote the book, who he wrote it for, and how it differs from other popular mathematics texts. It also discusses the gap between the arts and sciences, and includes testimonies from a physician and a lawyer about how mathematical thinking helped their professional work.
You should spend about 20 minutes on Questions 1–13, which are based on the passage below.
The passage contains three question types: Identifying Information (Q1–6), Sentence Completion (Q7–11), and Multiple Choice (Q12–13).
How the Other Half Thinks Full Reading Passage
Paragraph A
Beautiful, beginner-friendly passages can sometimes be found in otherwise challenging musical compositions, even in maths. Some discoveries in higher mathematics do not require familiarity with any specific branch of mathematics, not even the more common ones like algebra, geometry, and trigonometry. Instead, they may only necessitate some basic math (such as "the sum of two odd numbers is even") and logic. All eight chapters herein serve to demonstrate this phenomenon. The reasoning can be followed by any layperson.
Each chapter's reasoning makes use of no more than elementary mathematics. This way, every reader will have the opportunity to take part in a mathematical experience, enjoy mathematics for its aesthetic value, and become accustomed to the rational yet creative approach taken by mathematicians.
Paragraph B
One reason I wrote this book was to help those who might not have been exposed to real mathematics before developing an appreciation for mathematical thought. Not only do I wish to share some of the remarkable findings but also the logic that led to them. This book deviates from the norm of popular mathematics texts in that regard. There are even biographies of eccentric mathematicians. A number of other authors discuss significant mathematical applications. The reader is assumed to be familiar with algebra in works that delve into mathematical techniques.
Paragraph C
It is my sincere wish that this book will serve as a means toward healing the chasm that exists between the arts and the sciences, or, perhaps more accurately, involving the left (analytical, numerical) and right (intuitive) brain. It will become clear from the chapters that mathematics includes more than just analysis and computation; intuition or intuitive thinking also plays a crucial role. Because we rarely make use of either hemisphere's full potential, the purported gap can be reduced or eliminated in every individual. I use the examples of an artist structural engineer, a mathematician short story writer, an opera singer who published mathematical studies, and a mathematician who published short stories to demonstrate the breadth of human potential.
Paragraph D
Even though mathematics forms the backbone of other scientists' theories, they often leave it out of texts designed to explain their areas to the general public. Since mathematics is the ideal language for presenting the details in most science, the reader is left a tantalized observer rather than an active participant. This is true whether the topic at hand is the expanding universe, subatomic particles, or chromosomes. When a piece of the physical universe is ultimately grasped, its description often seems like a page in a mathematical manual, even though the broad. An outline of a scientific theory can be sketched intuitively.
Paragraph E
Even so, even a reader with little background in mathematics can grasp the essentials of mathematical reasoning. In-depth analysis, experimentation, and ideas that are characteristic of the mathematical mode of thought are presented here. These pages will be turned at a far more leisurely pace than a novel or newspaper. Having a pencil and paper handy might be useful for verifying statements and conducting experiments.
Paragraph F
I designed this book with two audiences in mind: people who liked math up until a bad experience, generally in fifth grade, put them off, and math nerds who will find a lot of fresh material to like. Readers who merely wish to hone their analytical abilities may also find value in this work. Profound, exact analysis is essential in many fields, including law and medicine. Each chapter provides opportunities to follow a well-developed path of reasoning. These two testimonies demonstrate the potential of mathematics to foster this skill:
Paragraph G
A doctor once wrote that his background in mathematics and its emphasis on analytical thought processes had prepared him well for his studies in medicine. To find a remedy to an issue in medicine, one must first conduct extensive research. Essential to such research is the ability to think through a problem carefully, to be systematic, and to rule out factors that are not relevant — skills that mathematical training develops. A lawyer made the same point: "Although I had no background in law not even one political science course I did well at one of the best law schools. I attribute much of my success there to having learned, through the study of mathematics, and, in particular, theorems, how to analyze complicated principles."
How the Other Half Thinks Reading Questions and Answers
Identifying Information (Q1–6)
The Reading Passage has seven sections, A–G. Which section contains the following information?
Write the correct letter, A–G, for questions 1–6 on your answer sheet.
NB You may use any letter more than once.
1. a reference to books that assume a lack of mathematical knowledge
2. the way in which this is not a typical book about mathematics
3. personal examples of being helped by mathematics
4. examples of people who each had abilities that seemed incompatible
5. mention of different focuses of books about mathematics
6. a contrast between reading this book and reading other kinds of publication
Sentence Completion (Q7–11)
Complete the sentences below.
Choose ONE WORD ONLY from the passage for each answer.
Write your answers for questions 7–11 on your answer sheet.
7. The author maintains that mathematical analysis necessitates ____________ thinking as well as analytical skills.
8. Aside from reading, the author suggests that non-mathematical readers should perform ___________.
9. A person with a _____________ would excel in certain musical and mathematical genres.
10. To keep their publications from being too dense, some ___________ had to gloss over the mathematics at the heart of their theories.
11. It was discovered by a lawyer that studying ___________ helped with law studies much more than other branches of mathematics.
Multiple Choice (Q12–13)
Choose the correct letter, A, B, C, or D.
12. Where in the brain can one find the ability to think analytically?
A. In the left hemisphere only
B. In the right hemisphere only
C. In both hemispheres
D. Neither hemisphere
13. What was the author's main reason for writing this book?
A. To help people who had not previously encountered real mathematics develop an appreciation for mathematical thought
B. To provide biographies of famous mathematicians
C. To explain advanced algebraic techniques to general readers
D. To describe applications of mathematics in science
