Math 300: History and Philosophy of Mathematics - Revision history

Dac47: moved Math 300: History & Philosophy of Mathematics to Math 300: History and Philosophy of Mathematics over redirect

2015-05-04T22:00:00Z

moved Math 300: History & Philosophy of Mathematics to Math 300: History and Philosophy of Mathematics over redirect

Ls5: moved Math 300: History and Philosophy of Mathematics to Math 300: History & Philosophy of Mathematics

2013-04-03T22:18:17Z

moved Math 300: History and Philosophy of Mathematics to Math 300: History & Philosophy of Mathematics

Ls5: moved Math 300 to Math 300: History and Philosophy of Mathematics

2013-04-03T22:08:27Z

moved Math 300 to Math 300: History and Philosophy of Mathematics

Cpg: /* Minimal learning outcomes */

2010-07-28T15:59:25Z

‎Minimal learning outcomes

Ls5: /* Minimal learning outcomes */

2009-04-01T17:54:05Z

‎Minimal learning outcomes

Cpg at 17:05, 1 April 2009

2009-04-01T17:05:56Z

Cpg at 14:20, 19 March 2009

2009-03-19T14:20:49Z

Cpg at 14:19, 19 March 2009

2009-03-19T14:19:17Z

Cpg at 14:18, 19 March 2009

2009-03-19T14:18:04Z

Cpg at 14:17, 19 March 2009

2009-03-19T14:17:36Z

← Older revision		Revision as of 15:59, 28 July 2010
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	</div>		</div>
		+
		+	=== Textbooks ===
		+	Possible textbooks for this course include (but are not limited to):
		+
		+	*

	=== Additional topics ===		=== Additional topics ===

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 <div style="-moz-column-count:2; column-count:2;">
-# '''Mathematics of ancient civilization''', especially of Babylon and Egypt with special reference to:
+# '''Mathematics of ancient civilizations''', especially of Babylon and Egypt with special reference to:
-#* '''Arithmetic''' representation of (natural) numbers in Egyptian, Chinese, Mayan and Roman numerals.  The evolution of our own (Indo-Arabic) number system.  Ability to do arithmetic in different number systems and conversion from one number system to another.
+#* '''Arithmetic'''. Representation of (natural) numbers in Egyptian, Chinese, Mayan and Roman numerals.  The evolution of our own (Indo-Arabic) number system.  Ability to do arithmetic in different number systems and conversion from one number system to another.
 #* '''Geometry'''.  Basic facts known at the time about triangles, circles, Pythagorean Theorem, Pythagorean triplets, Plimpton 322, Rhind Papyrus, proof of proportionality of sides of similar triangles, universality of π, and the formula for the area of a circle (without using integral calculus).
 # '''Greek Mathematics'''.  Evolution of Greek civilization with special reference to mathematics, its indebtedness to Babylonian and Egyptian math, life and contribution to math of Thales, Pythagoras, Zeno, Euclid, Apollonius, Eudoxus, Archimedes, Diophantus, Pappus and others.  Discussion of Euclid's ''Elements'', a sketch of his self-contained proof of Pythagorean Theorem.

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 # '''Mathematics of Medieval Europe'''.  Life and work of Fibonacci, especially his rabbit problem and congruent numbers (numbers that are areas of right triangles with all sides rational).
 # '''Mathematics of Renaissance'''.  Famous story behind Cardano's formula for solving cubic equations, discussion of the cube roots of unity, Cardano's formula and its proof.
-# '''Emergence of Modern Mathematics'''.  History of modern mathematical symbols (+, -, ×, etc.), introduction of letters for variables and constants by Viète and Descartes.  Invention of:
+# '''Emergence of Modern Mathematics'''.  History of modern mathematical symbols (+, -, ×, etc.), introduction of letters for variables and constants by Viète and Descartes.  The beginnings of modern number theory with Fermat. Invention of:
 #* Calculus, by Newton and Leibniz,
-#* Algebraic geometry, by Descartes and Fermat,
+#* Algebraic geometry, by Descartes and Fermat.
-#* The beginnings of modern number theory with Fermat.
+# '''Bernoullis and Euler'''.  Work of Euler and his standardization of current mathematical symbols and terminology.
-# '''Bermoullis and Euler'''.  Work of Euler and his standardization of current mathematical symbols and terminology.
 # '''French and German schools of Mathematics'''.  Gauss, Riemann, Cantor, Dirichlet, Weierstrass, . . ., and Cauchy, Lagrange, Laplace, Fourier, . . . .
 # '''Hilbert and his 23 Problems''', and their impact on 20th century math.

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 #* '''Arithmetic''' representation of (natural) numbers in Egyptian, Chinese, Mayan and Roman numerals.  The evolution of our own (Indo-Arabic) number system.  Ability to do arithmetic in different number systems and conversion from one number system to another.
 #* '''Geometry'''.  Basic facts known at the time about triangles, circles, Pythagorean Theorem, Pythagorean triplets, Plimpton 322, Rhind Papyrus, proof of proportionality of sides of similar triangles, universality of π, and the formula for the area of a circle (without using integral calculus).
-# '''Greek Mathematics:'''  Evolution of Greek civilization with special reference to mathematics, its indebtedness to Babylonian and Egyptian math, life and contribution to math of Thales, Pythagoras, Zeno, Euclid, Apollonius, Eudoxus, Archimedes, Diophantus, Pappus and others.  Discussion of Euclid's ''Elements'', a sketch of his self-contained proof of Pythagorean Theorem.
+# '''Greek Mathematics'''.  Evolution of Greek civilization with special reference to mathematics, its indebtedness to Babylonian and Egyptian math, life and contribution to math of Thales, Pythagoras, Zeno, Euclid, Apollonius, Eudoxus, Archimedes, Diophantus, Pappus and others.  Discussion of Euclid's ''Elements'', a sketch of his self-contained proof of Pythagorean Theorem.
 # '''Mathematics of Arabia'''.  Demise of the Greek math, Dark Ages in Europe, migration of Greek mathematicians to Arabia, translation of Greek texts into Arabic at the House of Wisdom at Baghdad.  Arab mathematicians, in particular al-Khwarizmi, their contribution to mathematics, including transmission of Indian mathematics to Europe.
 # '''Mathematics in China''' with special reference to the Chinese Remainder Theorem.

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 # '''French and German schools of Mathematics'''.  Gauss, Riemann, Cantor, Dirichlet, Weierstrass, . . ., and Cauchy, Lagrange, Laplace, Fourier, . . . .
 # '''Hilbert and his 23 Problems''', and their impact on 20th century math.
 </div>

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 # '''Mathematics of Arabia'''.  Demise of the Greek math, Dark Ages in Europe, migration of Greek mathematicians to Arabia, translation of Greek texts into Arabic at the House of Wisdom at Baghdad.  Arab mathematicians, in particular al-Khwarizmi, their contribution to mathematics, including transmission of Indian mathematics to Europe.
 # '''Mathematics in China''' with special reference to the Chinese Remainder Theorem.
-# '''Mathematics of Medieval India'''.  In
+# '''Mathematics of Medieval India'''.  Indian mathematicians, esp., Āryabhaṭa, Brahmagupta and Bhāskara, their solutions of the quadratic equation and the Pell equation, using the Pell equation to approximate square roots.
 </div>