MATH 410 History of Mathematics
Syllabus for Spring 2010

Tuesday, Thursday, 2:00PM – 3:20PM

325 Gildemeister Hall

Prerequisite: Passing grades in MATH160 and MATH210.

About This Course:  This course is intended to provide the student with an overview of the history of mathematics. We will emphasize the contributions made by various cultures across the globe and will ask the question: What is mathematics and who did it? We will also discuss the role of mathematics in these cultures, the surrounding history at the time, and the bias in historical accounts.

Expectations: Students who complete this course with a passing grade are expected to be able to demonstrate the following skills: (i) Knowledge of the historical development of mathematics, (ii) Understand the mathematics created and used by various peoples throughout history, (iii) Analyze, scrutinize and discuss possible mathematical writings, developments and arguments, (iv) Write a paper and present on a researched biographical topic.

Texts:   Math Through the Ages” by William P. Berlinghoff and Fernando Q. Gouvêa
“The Crest of the Peacock” by George Gheverghese Joseph (this book is out of print, so photocopies are available for purchase in the WSU book store).
Journey Through Genius: The Great Theorems of Mathematics” by William Dunham

Course Website:

Instructor: Dr. Eric Errthum                          Office: 124A Gildemeister Hall and 2B Lourdes Hall

Winona Email Username: eerrthum             Office Phone: 474-5775

Office Hours:  See schedule on my home page.

Grading:         Reading Quizzes                                                         100 points---------- 10%
                        Class Participation                                                      180 points---------- 18%
                        Midterms (3 @ 80 points)                                           240 points---------- 24%
                        Presentations (3 @ 50 points)                                     150 points---------- 15%
                        Biography Paper and Presentation                              200 points---------- 20%
                        Final                                                                            130 points---------- 13%
                                                                                                          1000 points total

Grades:  A = 90% (900 pts), B = 80% (800 pts), C = 70% (700 pts), D = 60% (600 pts)

Reading Quizzes:       Each class will start with a short quiz over the previously assigned readings. Completing the assigned readings is imperative for this class since lecture will only contain the main points and topics.

Class Participation:   A significant portion of each class will involve discussion of the previously assigned readings and discussion questions. You will be graded each day on your level of participation in these discussions. If you are absent you will receive a zero for the day, no exceptions.

Exams:     There will be three in-class exams and one final exam. The final exam will be in two parts. The first part being similar to the three midterms and only on material covered in the fourth part of the class (i.e. it’ll be the fourth midterm). The second part of the final will be a comprehensive essay section. Exam dates are tentative until officially announced in class. The final exam is tentatively scheduled for Tuesday, May 4, 1:00 – 3:00pm.

Presentations:            During the class period after each exam, students will each give a presentation. Each student will have 7 minutes to present on a topic chosen from a list given by the instructor (or a topic Okayed by the instructor). Make sure you come prepared as time will be limited. Make sure you come prepared as running short will hurt your grade. Powerpoint, PDF, or other electronic format encouraged. Sign up for a topic by following the links below.

Presentation Topics

Presentation I
Broken Numbers (Ages pp 85 – 90)
Something Less Than Nothing? (Ages pp 93 – 98)
By Tens and Tenths (Ages 101 – 104)
The Cossic Art (Ages pp 113 – 118)
Shapes by the Numbers (Ages pp 169 – 174)
Impossible, Imaginary, Useful (Ages pp 177 – 182)
Half is Better (Ages pp 185 – 190)

Presentation II
Hypatia of Alexandria (370?-415)
Elena Cornaro Piscopia (1646-1684)
Maria Agnesi (1718-1799)
Sophie Germain (1776-1831)
Mary Fairfax Somerville (1780-1872)
Ada Lovelace (1815-1852)
Charlotte Angas Scott (1848-1931)
Sofia Kovalevskaya (1850-1891)
Emmy Noether (1882-1935)

Presentation III
On Beauty Bare (Ages pp 155 – 160)
Strange New Worlds (Ages pp 193 – 198)
In the Eye of the Beholder (Ages pp 201 – 204)
What’s in a Game? (Ages pp 207 – 212)
Making Sense of Data (Ages pp 215 – 220)
Machines that Think? (Ages pp 223 – 228)
Beyond Counting (Ages pp 237 – 242)


Biography:     There will be a biography paper due near the end of the semester that you should be working on throughout (see schedule for due dates of various steps). The topic must be on a mathematician who was alive on December 7, 1941. Specifics of the paper:

1.      2500 words typed and well-written (i.e. correct spelling, complete sentences, good grammar, etc.)

2.      Must use at least one approved book source (an autobiography or complete biography) and 2 other sources (1 online source maximum)

3.      Must have information on at least the following aspects of their life:

a.       Early Life

b.      Mathematical Contributions (does not need to be overly technical)

c.       Their view on what mathematics is/should be

d.      Activities Outside of Mathematics

e.       Effects of WWII and/or Nazi Germany on Their Life

Possible Mathematicians: Richard Courant*, Paul Erdös*, Kurt Gödel*, Alexander Grothendieck*, David Hilbert*, Srinivasa Ramanujan*, John von Neumann*, Andre Weil*, Nicolas Bourbaki* (* indicates the instructor knows a biography you may use as your book source). The breakdown of points is: (Proposal: 10 points; Outline: 10 points; Rough Draft: 20 points; Final Paper: 90 points) Sign up for a topic here.

Presentation:  During the last week of classes you will have to give a 15 minute presentation on the same mathematician you wrote your biography paper on. The presentation will be worth 70 points.

Late/Missed Work: Late assignments or missed quizzes will result in a score of zero. There are no make-up quizzes. Make-up exams and presentations will be given at the discretion of the instructor. If you miss class, it is your responsibility to obtain notes and assignments from fellow students. If you have an unavoidable absence, please inform the instructor beforehand.

Desire2Learn:            Some course materials can be found on D2L.

Academic Dishonesty:  Any type of academic dishonesty (cheating, copying, plagiarism, etc.) will result in failure and will be reported to school authorities. If you are having trouble with an assignment, please see the instructor first. The instructor reserves the right to google any part of your written work to check for plagiarism.

Note:   This syllabus is subject to change if deemed necessary by the instructor.


Tentative Schedule of Events – Math 410

(subject to change)


Week Starting





What is Mathematics?

For Next Time, Read:
Peacock: Chapter 1 (pp 1 – 22)
(Total # pages: 22)

European vs. Non-European Roots

For Next Time, Read:

Ages: Beginnings (pp 1 – 14)
Peacock: Chapter 2 (pp 23 – 56)
(Total # pages: 48)


In the Beginning…


(Supplemental Reading: Andean Calculators)

For Next Time, Read:
Peacock: Chapter 3 (pp 57 – 90)
(Total # pages: 34)

Biography Proposal Due


For Next Time, Read:
Peacock, Chapters 4 & 5 (pp 91 – 129)
Ages: Keeping Count (pp 65 – 70)
(Total # pages: 45)


Presentation I Topic Due


For Next Time, Read:
Peacock: Part of Chapter 6 (pp 130 – 156)
Peacock: Part of Chapter 8 (pp 215 – 249)
 (Total # pages: 62)

Early China and India

For Next Time, Read:

All Presentation I topics (see page numbers above)
(Total # pages: 40)


Presentations I


Math and the Maya
The Story of Maths: The Language of the Universe



For Next Time, Read:
Ages: Greeks (pp 14 – 24)
Journey: Chapter 1 (pp 1 – 26)
(Total # pages: 36)

Beginning of Greeks

For Next Time, Read:
Peacock: Part of Chapter 7 (pp 180 – 188)
Journey: Chapter 2 (pp 27 – 60)
Ages: A Cheerful Fact (pp 139 – 144)
(Total # pages: 49)


Pythagorean Theorem

For Next Time, Read:
Journey: Chapter 3 (pp 61 – 83)
(Total # pages: 23)

Presentation II Topic Due

Number Theory

For Next Time, Read:
Peacock: Part of Chapter 7 (pp 188 – 196)
Journey: Chapter 4 (pp 84 – 112)
Ages: Measuring the Circle (pp 107 – 110)
(Total # pages: 42)



Presentations II


“Infinite Secrets”


For Next Time, Read:
Peacock: Part of Chapter 6 (pp 156 – 177)
Peacock: Part of Chapter 7 (pp 211 – 214)

(Total # pages: 26)




Classical China

For Next Time, Read:
Ages: India (pp 24 – 28)

Ages: Nothing Becomes a Number (pp 79 – 82)
Peacock: Part of Chapter 8 (pp 249 – 263)
Peacock: Part of Chapter 9 (pp 272 – 286)
(Total # pages: 39)

Biography Outline Due

Classical India

For Next Time, Read:
Journey: Epilogue of Chapter 5 (pp 129 – 132)
Peacock: Chapter 10 (pp 301 – 348)

Ages: Arabic (pp 28 – 32)
(Total # pages: 57)


Presentation III Topic Due

Arabic Contributions

For Next Time, Read:
Ages: Medieval Europe, 15th and 16th Centuries, Algebra (pp 32 – 42)
Ages: Reading and Writing Arithmetic (pp 73 – 76)
Ages: A Square and Things and Intrigue in Renaissance Italy
 (pp 127 – 130, 133 – 136)
Journey: Chapter 6 (pp 133 – 154)
(Total # pages: 45)


For Next Time, Read:

All Presentation III topics (see page numbers above)
(Total # pages: 40)


Presentations III

The Story of Maths: The Genius of the East



For Next Time, Read:
Ages: Calculus (pp 42 – 47)
Journey: Chapter 7 (pp 155 – 183)
(Total # pages: 35)

Rough Draft of Biography Papers Due


For Next Time, Read:
Journey: Chapters 8 & 9 (pp 184 – 222)
(Total # pages: 39)



For Next Time, Read:
Journey: Chapter 10 (pp 223 – 244)
(Total # pages: 22)

Number Theory II

For Next Time, Read:
Ages: Rigor, Abstraction and Math Today (pp 47 – 64)
Journey: Chapters 11 & 12 & The Afterword (pp 245 – 286)
(Total # pages: 60)


Current Mathematics

For Next Time, Read:

Ages: A Marvelous Proof (pp 147 – 152)

“The Proof”

or maybe

Fermat’s Last Theorem

Biography Papers Due

For Next Time, Read:

Other Students’ Biography Papers


Biography Presentations

Biography Presentations


Final Exam (Exam IV and Essay Questions)

Tuesday, May 4
1:00 – 3:00pm


Welcome to college math!


If this is your first math class taken in college, there are some important things you need to know. College math classes are run very differently from high school math classes. On the surface it may seem they are similar as you listen to the lecture and take notes, but there are significant underlying differences. Knowing these ahead of time can help you make the most of this coming semester.


#1: College math classes generally stay on the schedule in the syllabus. If there is one day allotted to the topic that is probably all of the class time that will be spent on it, even if “most” of the students “don’t get it.”


#2: It is expected that you will read the text and do the problems in order to learn the material, even if no one checks up on you. The instructor might never collect the homework, but that doesn’t mean it doesn’t affect your grade.


#3: You will sometimes be responsible for material in the textbook that is not covered in class. If there is a text reading and/or homework problems covering a concept that was not discussed in class, you are still expected to learn it. If you don’t understand it, make an appointment with your instructor for help.


#4: Some material is covered only in class, is not in the textbook, and may not have any homework problems on it. If you miss class, you may miss content that you are responsible to know. If you have an unavoidable absence, be sure to get the notes and any announcements from a classmate.


#5: There will be test questions that don’t look “just like the homework.” In college, you are expected to focus on learning the concepts, not just memorizing how to do certain types of problems. These concepts can – and will – appear in very different forms on tests and quizzes.


#6: At times you will be expected to be able to explain why a problem is done a certain way in addition to being expected to do the problem. As you work on problems in class and on homework, don’t be satisfied with getting the correct answer; ask yourself why that method is logical, and how you could explain that logic to someone else.


#7: Most importantly, you are responsible for your own learning. If you attend class faithfully, get the notes and announcements if you have an unavoidable absence, read the text, do the homework and question yourself (as in #6), and still don’t understand something, it is up to you to get the extra help you need. Visit the instructor during office hours or make a special appointment to ask questions, form a study group, etc. There are many resources and people willing and happy to help, but you need to take the initiative and seek out the help you need.


Welcome to college history!


If this is your first history class taken in college, there are some important things you need to know. College history classes are run very differently from high school history classes. On the surface it may seem they are similar as you listen to the lecture and take notes, but there are significant underlying differences. Knowing these ahead of time can help you make the most of this coming semester.


#1: Do not put off the readings. As much as possible, do the readings on the day they are assigned. Set aside plenty of time to complete the readings. Trying to make up hundreds or thousands of pages at the last minute will not work.


#2: Always read contextually. Ask yourself how each chapter and each source relates to one another, and to points discussed in class. As you read, outline the material. This will make it much easier for you to study for the exams.


#3: Always keep the main ideas in minds. When reading a chapter, ask yourself what the important points are. This may require you to wade through lots of historical details.


#4: In high school history classes, you probably had to do lots of memorization. This doesn't go away in college history, but there's much more to it. In college history, you'll be asked to understand the significance of historical events and people, and how these events and people relate to each other and to current events. Keep this in mind as you take notes, do the readings, and study for exams. It's important to keep in mind the significance of what you study. When studying an event, don't just memorize dates and names. Be able to explain why this event was important then and remains important today.


Good luck on a happy and successful semester!


Commitment to Inclusive Excellence:  WSU recognizes that our individual differences can deepen our understanding of one another and the world around us, rather than divide us. In this class, people of all ethnicities, genders, religions, ages, sexual orientations, disabilities, socioeconomic backgrounds, regions, and nationalities are strongly encouraged to share their rich array of perspectives and experiences.  If you feel your differences may in some way isolate you from WSU’s community or if you have a need of any specific accommodations, please speak with the instructor early in the semester about your concerns and what we can do together to help you become an active and engaged member of our class and community. 

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