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Title: Teaching a Course in the History of Mathematics Victor J. Katz University of the District of Columbia V. Frederick Rickey U. S. Military Academy


1
Teaching a Course in the History of
MathematicsVictor J. KatzUniversity of the
District of Columbia V. Frederick RickeyU. S.
Military Academy
2
Start readingnow !
3
Seminar Rules Apply
  • Ask any question at any time
  • But, heed the schedule
  • Email addresses are
  • fred-rickey_at_usma.edu
  • vkatz_at_udc.edu

4
Outline
  1. How to Organize a Course
  2. Approaches to Teaching History
  3. Resources for the Historian
  4. Student Assignments
  5. How to Prepare Yourself

5
I. How to Organize a Course
  1. Who is your audience?
  2. What are their needs?
  3. What are the aims of your course?
  4. Types of history courses
  5. Textbooks for survey courses with comments
  6. Textbooks for other types of courses
  7. The design of your syllabus
  8. Is a field trip feasible?
  9. History of Math Courses on the Web

6
II. Approaches to Teaching History
  1. Internal vs. External History
  2. Whig History
  3. The Role of Myths
  4. Ideas from non-Western sources
  5. Teaching ethnomathematics
  6. Teaching 20th and 21st century mathematics

7
III. Resources for the Historian
  • Books, journals, and encyclopedias
  • Web resources
  • Caveat emptor

8
IV. Student Assignments
  • Learning to use the library
  • What to do about problem sets?
  • Student projects
  • Possible student paper topics
  • Projects for prospective teachers
  • Exams

9
V. How to Prepare Yourself
  • Start a reading program now!
  • Collect illustrations
  • Outline your course day by day
  • Get to know your library and librarians
  • Advertising your course
  • Counteract negative views
  • Record keeping

10
Are there other topics you would like us to
discuss?
  • Note We are not teaching history here

11
I. How to Organize a Course
  1. Who is your audience?
  2. What are their needs?
  3. What are the aims of your course?
  4. Types of history courses
  5. Textbooks for survey courses with comments
  6. Textbooks for other types of courses
  7. The design of your syllabus
  8. Is a field trip feasible?
  9. History of Math Courses on the Web

12
I.1. Who is your audience?
  • What level are your students?
  • How good are your students?
  • What type of school are you at?
  • How much mathematics or general history do they
    know? Answer Not enough!
  • Is the course for liberal arts students?
  • What will they do after graduation?

13
I.2. What are their needs?
  • If your students are prospective teachers, what
    history will benefit them?
  • Why are the students taking the course?
  • How much fact do the students need to know?
  • Is this a capstone course for mathematics majors
    that is intended to tie together what they have
    learned in other course?

14
PROSPECTIVE HIGH SCHOOL TEACHERS
  • Teach more mathematics
  • Make sure to deal with the history of topics in
    the high school curriculum
  • Discuss the use of history in teaching secondary
    mathematics courses
  • Stress the connections among various parts of the
    curriculum

15
OTHER MATHEMATICS MAJORS
  • History as a capstone course helps to tie
    together what they have learned
  • Graduate school and academia
  • Need to understand the development of ideas and
    how to use these in future teaching
  • How and why abstraction became so important in
    the nineteenth century

16
1.3. AIMS OF THE COURSE
  • To give life to your knowledge of mathematics.
  • To provide an overview of mathematics
  • To teach you how to use the library and internet.
  • To indicate how you might use the history of
    mathematics in your future teaching.
  • To improve your written communication skills in a
    technical setting.

17
MORE AIMS
  • To show that mathematics has been developed in
    virtually every literate civilization in history,
    as well as in some non-literate societies.
  • To compare and contrast the approaches to
    particular mathematical ideas among various
    civilizations.
  • To demonstrate that mathematics is a living field
    of study and that new mathematics is constantly
    being created.

18
I.4    Types of History Courses
  • Survey
  • Theme
  • Topics
  • Sources
  • Readings
  • Seminar

19
I.5 Survey Texts
  • Boyer
  • Burton
  • Calinger
  • Cooke
  • Eves
  • Grattan-Guinness
  • Katz
  • Hodgkin
  • Suzuki

20
1.6. Textbooks for other courses
  • Dunham, Journey through genius the great
    theorems of mathematics
  • Berlinghoff and Gouvêa, Math through the ages A
    gentle history for teachers and others
  • Bunt, Jones, and Bedient, The historical roots of
    elementary mathematics
  • Joseph,The crest of the peacock non-European
    roots of mathematics
  • Struik, A concise history of mathematics. New
    York

21
Sourcebooks
  • John Fauvel and Jeremy Gray, The History of
    Mathematics A Reader
  • Ronald Calinger, Classics of Mathematics
  • Jacqueline Stedall, Mathematics Emerging A
    Sourcebook 1540-1900
  • Victor J. Katz, ed., The Mathematics of Egypt,
    Mesopotamia, China, India, and Islam A
    Sourcebook

22
I.7. The design of your syllabus
  • Text
  • Aims
  • Outline
  • Readings
  • Assignments
  • Texts
  • Plagiarism

23
I. 8    Is a Field Trip Feasible?
  • Visit a rare book room
  • Visit a museum
  • Visit a book store

24
I.9. HM Courses on the Web
  • Many individuals have placed information about
    their courses on the web.
  • See the url on p. 1 of the handout, which will
    take you to Rickeys pages on this minicourse.
  • Note especially the sources course of Gary
    Stoudt, whose url is on p. 6 of the handout.

25
II. Approaches to Teaching History
  1. Internal vs. External History
  2. Whig History
  3. The Role of Myths
  4. Ideas from non-Western sources
  5. Teaching ethnomathematics
  6. Teaching 20th and 21st century mathematics

26
II.1. Internal History
  • Development of ideas
  • Mathematics is discovered (Platonism)
  • History written by mathematicians
  • Mathematics is the same, whether created in
    Babylon, Greece, or France i.e., mathematics is
    universal

27
II.1. vs. External History
  • Cultural background
  • Mathematics is invented
  • History written by historians
  • Mathematics influenced by ambient culture
    (Story of Maclaurin)
  • Biographies

28
II.2. Whig History
  • It pictures mathematics as progressively and
    inexorably unfolding, brilliantly impelled along
    its course by a few major characters, becoming
    the massive edifice of our present inheritance.
  • Does history then only include ideas that were
    transmitted somehow to the present or had
    influence later on?
  • Or do we try to understand mathematical ideas in
    context?

29
Examples of ideas that were probably not
transmitted
  • Indian development of power series
  • Babylonian solution of quadratic equations
  • Islamic work on sums of integral powers
  • Chinese solution of simultaneous congruences
  • Gausss notebooks

30
Examples of ideas that probably were transmitted
  • Basic ideas of equation solving
  • Trigonometry, both plane and spherical
  • Basic concepts of combinatorics

31
II.3. The Role of Myths
  • What myths do we tell?
  • What myths do we want future teachers to tell
    their students?
  • Do we tell the truth and nothing but the truth?
    (We cannot tell the whole truth.)

32
II.4. Ideas from non-Western sources
33
Why non-Western Mathematics?
  • Not all mathematics developed in Europe
  • Some mathematical ideas moved to Europe from
    other civilizations
  • Relevance of Islam, China, India today
  • Mathematics important in every literate culture
  • Compare solutions of similar problems
  • Diversity of your students and your students
    prospective students

34
Chinese Remainder Theorem
  • Why is it called the Chinese Remainder Theorem?
  • The first mention of Chinese mathematics in a
    European language was in 1852 by Alexander Wylie
    Jottings on the Science of the Chinese
    Arithmetic
  • Among the topics discussed is the earliest
    appearance of what is now called the Chinese
    Remainder problem and how it was initially solved
    in fourth century China, in Master Suns
    Mathematical Manual.

35
Chinese Remainder Theorem
  • We have things of which we do not know the
    number if we count them by threes, the remainder
    is 2 if we count them by fives, the remainder is
    3 if we count them by sevens, the remainder is
    2. How many things are there?
  • If you count by threes and have the remainder 2,
    put 140. If you count by fives and have the
    remainder 3, put 63. If you count by sevens and
    have the remainder 2, put 30. Add these numbers
    and you get 233. From this subtract 210 and you
    get 23.
  • For each unity as remainder when counting by
    threes, put 70. For each unity as remainder when
    counting by fives, put 21. For each unity as
    remainder when counting by sevens, put 15. If
    the sum is 106 or more, subtract 105 from this
    and you get the result.

36
Indian proof of sum of squares
  • A sixth part of the triple product of the
    term-count n plus one, that sum plus the
    term-count, and the term-count, in order, is the
    total of the series of squares. Being that this
    is demonstrated if there is equality of the total
    of the series of squares multiplied by six and
    the product of the three quantities, their
    equality is to be shown.

37
Teaching a Course in the History of
MathematicsVictor J. KatzUniversity of the
District of Columbia V. Frederick RickeyU. S.
Military Academy
38
Islamic Proof
  • This example is taken from the Book on the
    Geometrical Constructions Necessary to the
    Artisan by Abu al-Wafaal-Buzjani (940-997). He
    had noticed that artisans made use of geometric
    constructions in their work. But, A number of
    geometers and artisans have erred in the matter
    of these squares and their assembling. The
    geometers have erred because they have little
    practice in constructing, and the artisans have
    erred because they lack knowledge of proofs.

39
Islamic Proof
  • I was present at some meetings in which a
    group of geometers and artisans participated.
    They were asked about the construction of a
    square from three squares. A geometer easily
    constructed a line such that the square of it is
    equal to the three squares, but none of the
    artisans was satisfied with what he had done.

40
Islamic Proof
  • Abu al-Wafa then presented one of the
    methods of the artisans, in order that the
    correct ones may he distinguished from the false
    ones and someone who looks into this subject will
    not make a mistake by accepting a false method,
    God willing. But this figure which he constructed
    is fanciful, and someone who has no experience in
    the art or in geometry may consider it correct,
    but if he is informed about it he knows that it
    is false.

41
Islamic Proof
42
Why Was Modern Mathematics Developed in the West?
  • Compare mathematics in China, India, the Islamic
    world, and Europe around 1300
  • Europe was certainly behind the other three
  • Ideas of calculus were evident in both India and
    Islam
  • But in next 200 years, development of mathematics
    virtually ceased in China, India, and Islam, but
    exploded in Europe
  • Why?

43
II.5. Teaching Ethnomathematics
  • Mathematical Ideas of traditional peoples
  • What is a mathematical idea?
  • Idea having to do with number, logic, and
    spatial configuration and especially in the
    combination or organization of those into systems
    and structures.
  • Can these mathematical ideas of traditional
    peoples be related to Western mathematical ideas?

44
Examples of Ethnomathematics
  • Mayan arithmetic and calendrical calculations
  • Inca quipus
  • Tracing graphs among the Bushoong and Tshokwe
    peoples of Angola and Zaire
  • Symmetries of strip decorations
  • Logic of divination in Madagascar
  • Models and maps in the Marshall Islands

45
Books on Ethnomathematics
  • Marcia Ascher, Ethnomathematics A Multicultural
    View of Mathematical Ideas (1991)
  • Marcia Ascher, Mathematics Elsewhere An
    Exploration of Ideas Across Cultures (2002)

46
New concepts
II.6. TEACHING 20TH AND 21ST CENTURY MATHEMATICS
  • Set Theory and Its Paradoxes
  • Axiomatization
  • The Statistical Revolution
  • Computers and Computer Science

47
Recently resolved problems
II.6. TEACHING 20TH AND 21ST CENTURY MATHEMATICS
  • Four Color Problem
  • Classification of Finite Simple Groups
  • Fermats Last Theorem
  • Poincaré Conjecture

48
Unresolved problems
II.6. TEACHING 20TH AND 21ST CENTURY MATHEMATICS
  • Hilberts 1900 list of Problems
  • Which Problems Are Still Unresolved?
  • See Ben Yandell, The Honors Class (2002)
  • Clay Millennium Prize Problems
  • Riemann Hypothesis
  • Birch and Swinnerton-Dyer Conjecture
  • See K. Devlin, The Millennium Problems
    (2002)

49
III. Resources for the Historian
  1. Books, journals, and encyclopedias
  2. Web resources
  3. Caveat emptor

50
Twenty Scholarly Books
  • Jens Høyrup, Lengths, Widths, Surfaces A
    Portrait of Old Babylonian Algebra and Its Kin
    (2002)
  • Eleanor Robson Mathematics in Ancient Iraq A
    Social History (2008)
  • Kim Plofker Mathematics in India 500 BCE
    1800 CE (2009)
  • Jean-Claude Martzloff, A History of Chinese
    Mathematics, translated by Stephen S. Wilson
    (1997)

51
Books
  • Victor J. Katz, ed., The Mathematics of Egypt,
    Mesopotamia, India, China, and Islam A
    Sourcebook (2007)
  • D. H. Fowler, The Mathematics of Plato's Academy
    A New Reconstruction (1987, 1999)
  • S. Cuomo, Ancient Mathematics (2001)
  • Reviel Netz, The Transformation of Mathematics in
    the Early Mediterranean World From Problems to
    Equations (2004)

52
Books
  • J. Lennart Berggren, Episodes in the Mathematics
    of Medieval Islam (1986)
  • Glen Van Brummelen, The Mathematics of the
    Heavens and the Earth The Early History of
    Trigonometry (2009)
  • Jeremy Gray, Worlds Out of Nothing A Course in
    the History of Geometry in the 19th Century
    (2007)
  • Hans Wussing, The Genesis of the Abstract Group
    Concept (1984)

53
Books
  • Ivor Grattan-Guinness, ed. From the Calculus to
    Set Theory, 1630-1910 An Introductory History
    (1980)
  • C. H. Edwards, The Historical development of the
    calculus (1979)
  • Judith V. Grabiner, The Origins of Cauchy's
    Rigorous Calculus (1981)
  • Stephen M. Stigler, The History of Statistics
    (1986)

54
Books
  • Gerd Gigerenzer et al, The Empire of Chance How
    Probability Changed Science and Everyday Life
    (1989)
  • Ed Sandifer, The Early Mathematics of Leonhard
    Euler (2007)
  • Robert Bradley and C. Edward Sandifer, eds.,
    Leonhard Euler Life, Work and Legacy (2007)
  • Ivor Grattan-Guinness, ed., Landmark Writings in
    Western Mathematics, 1640-1940 (2005)

55
Ten Popular Books
  • Derbyshire, John. Prime Obsession Bernhard
    Riemann and the Greatest Unsolved Problem in
    Mathematics, 2003.
  • Dunham, William. The Calculus Gallery
    Masterpieces from Newton to Lebesgue, 2005
  • Havil, Julian. Gamma Exploring Eulers
    Constant, 2003.
  • Maor, Eli Trigonometric Delights, 1998.
  • Netz, Reviel and William Noel. The Archimedes
    Codex, 2007

56
Popular Books
  • Nahin, Paul J. An Imaginary Tale The Story of
    ?1, 1998.
  • __________ When Least Is Best How
    Mathematicians Discovered Many Clever Ways to
    Make Things as Small (or as Large) as Possible,
    2003.
  • Salsburg, David. The Lady Tasting Tea How
    Statistics Revolutionized Science in the
    Twentieth Century, 2001.
  • Sobel, Dava. Longitude The True Story of a
    Lone Genius Who Solved the Greatest Scientific
    Problem of His Time, 1995.
  • Wilson, Robin. Four Colours Suffice How the
    Map Problem Was Solved, 2002.

57
III.1.a. Collection
58
Table of Contents
  • Archimedes
  • Combinatorics
  • Exponentials and Logarithms
  • Functions
  • Geometric Proof
  • Lengths, Areas, and Volumes
  • Linear Equations
  • Negative Numbers
  • Polynomials
  • Statistics
  • Trigonometry

59
III.1.b. History Journals
  • Historia Mathematica
  • Isis
  • Archive for History of Exact Sciences
  • The British Journal for the History of Science
  • Annals of Science
  • History of Science

60
III.1.b. Popular Journals
  • The MAA journals
  • Mathematical Intelligencer
  • Physics Teacher
  • Scientific American
  • Mathematical Gazette
  • Bulletin of the British Society of the History of
    Mathematics

61
III.1.c. Encyclopedias
  • Companion encyclopedia of the history and
    philosophy of the mathematical sciences, edited
    by I. Grattan-Guinness
  • Dictionary of Scientific Biography
  • The Encyclopaedia Britannica, 11th ed
  • The Encyclopedia of Philosophy
  • Dictionary of American Biography,

62
III.2. WEB RESOURCES
  • These are so abundant and the search engines are
    so good, that it seems futile to attempt anything
    comprehensive.
  • Here are a few especially useful ones.

63
(No Transcript)
64
Rome Reborn Earliest Extant Euclid, 888
www.ibiblio.org/expo/vatican.exhibit/Vatican.exhib
it.html
65
The Euler Archivehttp//www.math.dartmouth.edu/
euler/
E53 Solutio problematis ad geometriam situs
pertinentis
66
http//www.math.ubc.ca/people/faculty/cass/Euclid
/byrne.html
67
http//www.lib.cam.ac.uk/RareBooks/PascalTraite/
68
David Joyces History of Mathematics Homepage
  • http//aleph9.clarku.edu/djoyce/
  • mathhist/

69
IV. Student Assignments
  • Learning to use the library
  • What to do about problem sets?
  • Student projects
  • Possible student paper topics
  • Projects for prospective teachers
  • Exams

70
IV.1. Learning to use the library
  • Tour of library
  • Your mathematician
  • Prize nomination
  • Vita

71
IV.2. Problem Sets
  • Solve a problem as it was solved in a particular
    time period
  • Complete the development of a particular idea or
    procedure
  • Solve an old problem using modern tools and
    compare methods
  • Generalize an old problem solving procedure

72
Discussion Problems
  • Compare and contrast methods
  • Develop a lesson for the classroom based on a
    particular historical development
  • Discuss the pedagogy of an old textbook

73
IV.3. Projects
  • Written projects and/or oral reports?
  • Joint or individual projects?

74
IV.4. Possible Student Paper Topics
  • Bourbaki
  • Julia Robinson and Hilbert's tenth problem
  • Alan Turing
  • Dürer's Polyhedra
  • The Four Color Problem
  • Holbein's Ambassadors
  • Daniel Bernoulli the spread of smallpox

75
IV.5. Projects for Prospective Teachers
  • Compare the Babylonian, Mayan, and Hindu-Arabic
    place-value systems in their historical
    development and their ease of use. Devise a
    lesson on this.
  • Analyze the history of the limit concept from
    Eudoxus to the mid-eighteenth century, including
    Berkeley's criticisms and Maclaurin's response.
    Create a lesson.
  • Discuss how the history of the solution of cubic
    equations from the Islamic period through the
    work of Lagrange can be used in algebra classes.
  • Compare the teaching of algebra (or geometry) in
    the eighteenth century and the twentieth by
    studying textbooks.

76
IV. 6. Exams
  • Mathematical Problems
  • Short Answer Questions
  • Multiple Choice Questions
  • Essay Questions

77
Mathematical Problems
  • 1. Translate a Babylonian problem and solution
    into modern terms
  • 2. Solve a quadratic problem of Abu Kamil by
    first converting it into one of the six types of
    quadratic equations and then using the method for
    that type. For example, suppose 10 is divided
    into two parts, each one of which is divided by
    the other, and the sum of the quotients is 4 ¼.
    Find the two parts.
  • 3. Use Fermats method to find the maximum of
  • bx x3

78
Mathematical Problems
  • 4. Find the relationship of the fluxions of x
    and y on the curve x2 xy y3 7 using one of
    Newtons procedures.
  • 5. Derive the quotient rule of calculus by an
    argument using differentials.
  • 6. Give a geometric argument using
    differentials and similar triangles to show that
  • d(sin x) cos x dx.
  • 7. Show that one can solve the cubic equation
  • x3 d bx2 by intersecting the hyperbola
  • xy d and the parabola y2 dx db 0.

79
Short Answer Questions
  • 1. Order the following mathematical discoveries
    by their approximate date, beginning with the
    earliest
  • a. Solution of the system of equations which we
    express as xy a, x y b.
  • b. Earliest explicit expression of the
    multiplicative rule for combinations.
  • c. Development of the base 60 place value system.
  • d. Development of the base 10 place value system.
  • e. First statement of the parallel postulate.
  • f. First extant rigorous proof of the rule for
    combinations expressed in b.

80
Short Answer Questions
  • 2. State one mathematical contribution of each of
    the following Cardano, Bombelli, Viete,
    Harriot.
  • 3. What is Cardanos Ars Magna and why is it
    important?
  • 4. Trigonometry was originally developed to
    _____________________.

81
Essay Questions
  • 1. Outline the major contributions to
    trigonometry of the civilizations of Greece,
    India, and Islam.
  • 2. Today, mathematics is often thought of as the
    intellectual exercise of proving theorems using
    logical reasoning and beginning with explicitly
    stated definitions and axioms. Were the
    Babylonians and the Egyptians, then, doing
    mathematics? Explain.
  • 3. Describe the proof method called today the
    method of mathematical induction. Was the proof
    by Levi ben Gerson giving the formula for the
    number of permutations of a set of n objects a
    proof by mathematical induction? Why?

82
Essay Questions
  • 4. Is mathematics invented or discovered?
    Discuss with reference to at least four
    mathematical concepts discussed this semester.
  • 5. Compare and contrast Newtons and Leibnizs
    versions of the calculus. In your answer,
    include ideas in differentiation, integration,
    solving differential equations, and applications
    to physical problems.
  • 6. Compare and contrast the use of axioms by
    Euclid with the use of axioms around the turn of
    the twentieth century. For the latter period,
    you may pick one or two axiom sets to provide a
    focus for your discussion.
  • 7. Why is rigor in analysis so important?
    After all, Newton and Leibniz worked out the
    basics of the calculus without it. Give examples
    to support your argument.

83
V. How to Prepare Yourself
  • Start a reading program now!
  • Collect illustrations
  • Outline your course day by day
  • Get to know your library and librarians
  • Advertising your course
  • Counteract negative views
  • Record keeping

84
Start readingnow !
85
V.1. Start a reading program now!
  • Read a survey text
  • Read journal articles
  • Read deeply in the history of a mathematical
    field you know well

86
How to Learn More History
  • Go to talks at meetings
  • Join the Canadian Society for the History and
    Philosophy of Mathematics and the British Society
    for the History of Mathematics
  • Join/start a seminar in the history of mathematics

87
V.2. Collect illustrations
  • Pictures of mathematicians.
  • Title pages of famous works.
  • Significant pages from important works.
  • Maps.
  • Quotations from famous mathematicians.

88
Emilie du Chatelet
89
Paciolis Summa
90
Reischs Margarita Philosophica
91
V.3. Outline Your Course Day by Day
  • Decide on nature of course (Chronological,
    Themed, Combination)
  • Pick out key general concepts and order them
  • For each key concept, pick out specific topics to
    cover
  • Choose a topic or topics for each available day
  • Pick materials related to each chosen topic
  • Give yourself flexibility, for undoubtedly you
    will have planned too much

92
Descartes
93
Outline for day xx    Descartes on Analytic
Geometry
  • Biographical information worth mentioning
  • Attended a good school. Recent work of Galileo
    and his telescope was discussed.
  • A sickly lad. Lay in bed.
  • Fly and analytic geometry. True?
  • Importance of contact with the Dutch. Latin.
  • Queen Christina of Sweden. Death.

94
Scientific work of Descartes
  • Philosophia mathematica.  Newton used this title.
  • Method. Cogito ergo sum. Tell Ari Katz joke.
  • Geometry is an appendix. You can read it.
    Translations.
  • Optics Snell's law, rainbow.
  • Started analytic geometry. Oblique axes. xyz for
    variables. Exponent notation
  • Curves geometric vs. mechanical. Examples.
  • He went from geometry to algebra, not v.v.
  • Had a method to solve any problem (and Newton
    believed him!).
  • Folium of Descartes. Fermat has a better method
    for tangents.
  • Says you can't do arc length. Set up for van
    Heuraet and Newton.

95
Powerpoint to Prepare
  • Portraits
  • Seated, Schooten, stamps, Vic Norton's cartoon on
    aliasing.
  • Title pages
  • Geometrie 1637, 1649, 1659. Newton read the
    second Latin edition.
  • Translations Smith-Latham, Olscamp.
  • Quotations
  • Rules of problem solving. For prospective
    teachers especially.
  • Newton on reading Descartes.
  • This method will solve all problems.
  • Selected Pages
  • Solution of quadratic equations.
  • Conchoid is geometric.
  • Finding tangents by the two circle method.
  • Heuraet on arc length from second Latin edition
    (1659).
  • Folium of Descartes. 1638 definition. Graphs of
    Newton and L'Hospital.

96
  • Things to take to class to pass around
  • Smith-Latham translation of Geometry.
  • Olscamp translation of the whole Method.
  • Polya's How to Solve It.
  • Things to read before class
  • Sections of the text the students are to read.
  • The DSB article on Descartes.
  • Look at J. F. Scott's, The scientific work of
    René Descartes, 1952
  • Read section on Descartes in Grattan-Guinnesss
    Landmarks

97
V.4. Get to know your library and librarians
  • Look at every book
  • Find the specialized librarians
  • Tell them your interests
  • Ask them to help your students
  • Be determined to find answers
  • Visit a rare book room

98
V.5. Advertising your course.
  • Talk to former students
  • Send email to majors
  • Post flyers
  • Talk to colleagues

99
V.6. Counteract Negative Views
  • Among some mathematicians the history of
    mathematics is not regarded as a serious pursuit.
  • It is worth your while to spend some time talking
    to your colleagues about your course. Point out
    to them that you are doing significant amounts of
    mathematics in your course (give some
    illustrations). Point out that it is not a course
    in anecdotes.
  • Students must master a great deal of material and
    they are required to write about mathematics in a
    way that shows that they have mastered the
    details.

100
V.7 Record keeping
  • Immediately record full reference for items you
    photocopy
  • Record what references you use for each class
  • Record how you could improve the class (and what
    not to do again)

101
Start readingnow !
102
  • PowerPoint and additional information available
    at
  • http//www.dean.usma.edu/
  • departments/math/people/
  • rickey/hm/mini/default.html

103
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  • Using Historical Topics of Mathematics
    Effectively in the High School Curriculum
  • David Kullman (Miami University of Ohio) will
    host a workshop on June 23-25, 2009 at Bluffton
    University. The cost is 125 which includes
    lunches.
  • Contact Duane Bollenbacher at
    bollenbacher_at_bluffton.edu or 419-358-3296
  • Further information will appear on the
    webpage of the Ohio Section of the MAA.

104
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  • History of Undergraduate Mathematics in America
    (HUMA II)
  • Meeting is planned for the summer of 2010 at West
    Point.
  • Your research contributions are welcome.
  • Contact Fred Rickey.
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