Introducing the History of Mathematics: An Italian Experience Using Original Documents - Contents of Students' Volume

            As a brief introduction to the content and format of Fare mathematica some  excerpts are given in English translation:

                            The Table of Contents from the Students’ Volume:

CONTENTS

Preface by Fulvia Furinghetti

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Introduction for students.

CHAPTER 1: FROM ARITHMETIC TO ALGEBRA - Numeration: Egyptians; Babylonians; Greeks; Romans; Mayas; Indians, at last; Who invented binary numbers? - Operations and non-negative integers: Middle Ages and Renaissance - Not only non-negative numbers: Fractions in Egypt: the Horus’ eye; How Egyptians wrote fractions; Decimals and Arabs; Decimals in Europe - The arithmetic triangle: Chinese, Arabs, Europeans… - Curious problems: Let’s solve together; Other problems: the text; Other problems: the solutions - “False” numbers: In sixteenth-century Italy; A woman grapples with mathematics - From words to symbols: A great Arabian mathematician; Diophantus left a mark; All of them are equations; A “recipe” to solve an equation; The science of “literal calculus”; Philosopher, physician and… mathematician - Problems and equations: Linear and quadratic problems - Bombelli and the number i: Is it a number? - Logarithms: An ancient idea; An authoritative answer - And more…  evolution of symbols.

CHAPTER 2 – FACES OF GEOMETRY - Arithmetic and geometry: figurate numbers: Polygonal numbers; Pythagorean terns; Ingenious ways to obtain Pythagorean terns - Pythagorean theorem: A walk through history: sides and squares…; … a problem in the Renaissance…; …problems and equations - Far points: About towers and other buildings; How to bore a tunnel and not come out in the wrong place - Square root of 2: How did they do it? - pi: What is the true value? - Archimedes: A volley of propositions; The area of the circle and the method of exhaustion - Cartesian coordinates?…: In the fourteenth century; One of the fathers - Geometry, of Euclid and not: An authoritative introduction, but…; The Elements: almost a Bible; Two millennia later - Trigonometry: From a sixteenth-century book - What is topology?: A new geometry; The problem of Königsberg’s bridges; The explanation of Euler - And more… solid numbers.

CHAPTER 3: THEMES OF MODERN MATHEMATICS - Logic: an ancient but current science: What are logical connectives?; The art of… reasoning; Mathematics takes possession of logic - Logic to build numbers: Gottlob Frege and Bertrand Russell - Let’s measure uncertainty: Galileo and a problem about the casting of three dice; Epistolary interchanges; The classical conception of probability; Other conceptions of probability - Infinity: Runners, arrows, hares, tortoise,…; The whole is not greater than the part; Infinite is a source of other paradoxes; Let’s arrange our knowledge - Cantor’s paradise: Real numbers are more than integers; Cantor in Hilbert’s opinion - Infinitesimals before Newton: The circle; The torus; The indivisibles - Limits, derivatives, integrals (I’m sorry if it is too little): Isaac Newton - We don’t stop… history continues…