MESSAGES: (as of 12/7/'15) ========================================================================== ========================================================================== Welcome to MATH 432: History of Mathematics This is the "message link": http://userpages.umbc.edu/~seidman/f15/m-432 >>>>> Note: I will abbreviate by writing this as */m-432 <<<<<< ========================================================================== ========================================================================== http://www.math.buffalo.edu/mad/Ancient-Africa/egyptianfractionslinks.html http://www-history.mcs.st-and.ac.uk/Indexes/HistoryTopics.html http://aleph0.clarku.edu/~djoyce/java/elements/toc.html ========================================================================== http://www.storyofmathematics.com/ https://www.youtube.com/watch?v=YsEcpS-hyXw https://www.youtube.com/watch?v=h-DV26x6n_Q https://whoinventedcalculus.wordpress.com/ (and related ...) https://www.youtube.com/watch?v=fEWj93XjON0 (Euler) https://www.youtube.com/watch?v=YaUlqXRPMmY (Feynman) http://plato.stanford.edu/entries/computability/ (logic + complexity) ========================================================================== >>> HW? Look at https://www.quantamagazine.org/20151124-kadison-singer-math-problem/ I would like some class discussion of whether (and in what way) this represents a significant new pattern of development in Mathematics. Is this related to the growth of the Internet? To what extent does it emphasize tho role of social interaction (e.g., travel and communication) in the development of Mathematics? >>> Conversely, look at http://www.nytimes.com/2012/07/29/opinion/sunday/is-algebra-necessary.html Does this suggest that noncommercial Mathematics is an elite activity? ========================================================================== >>> Take-home `exam' (=Summary self-assessment.) [due Thursday, 12/10] >>> We discussed this briefly in class Thursday, but I am also providing more detail in http://userpages.umbc.edu/~seidman/f15/432summary. >>> [Sorry -- I had thought I had already posted this last week.] ========================================================================== ========================================================================== archive: older items | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | \| |/ \ / V ========================================================================== ========================================================================== >>>>> ARCHIVE: older items in chronological order (but split as messages and assignments) ========================================================================== ========================================================================== >>>>>> MESSAGES, IMPORTANT MISCELLANY <<<<<<<< ========================================================================== ========================================================================== >>>>> Bookmark this link (userpages.umbc.edu/~seidman/f15/m-432) which will be one of my consistent ways of communicating with you outside class --- check this often! ========================================================================== >>> For the HW, you are expected to give enough explanation/work along with the bare answer to make it clear you understand things. This also makes it possible to correct misunderstandings and to give partial credit. ========================================================================== >>> IMPORTANT: If you want to send me things by e-mail, do NOT send them as Word files (.doc or .docx). I will only be able to read them if they are plain text (as in the body of an e-mail) or .pdf files as attachments; sending a .tex source file as a plain text attachment is also acceptable. [Indeed, I recommend learning LaTeX for technical writing.] ========================================================================== >>> There will be a "Quiz#0" at the first class meeting. This will not count for grading, but will give me some idea of backgrounds, etc. ========================================================================== >>> READ: http://userpages.umbc.edu/~seidman/f15/blurb-432.pdf ========================================================================== ========================================================================== >>> HW assignments will be given through this link and due on Tuesdays >>> For the HW, you are expected to give enough explanation/work along with the bare answer to make it clear you understand things. This also makes it possible to correct misunderstandings and to give partial credit. ========================================================================== >>> The Syllabus is now available at */432-syllabus-f15.pdf --- i.e. userpages.umbc.edu/~seidman/f15/432-syllabus-f15.pdf >>> Some URL links are available at */432links.html WARNING: That is an old file and many don't work now. ========================================================================== http://www.math.buffalo.edu/mad/Ancient-Africa/egyptianfractionslinks.html http://www-history.mcs.st-and.ac.uk/Indexes/HistoryTopics.html http://aleph0.clarku.edu/~djoyce/java/elements/toc.html ========================================================================== >>> As discussed in class, the topic for our first "major writing assignment" will be what it means to "understand the History of Math" (in the sense of understanding how modern math developed to be as it is). I will consider most important here the selection and organization of material. In this connection (although not specifically related to Math) is an article: http://www.newyorker.com/magazine/2015/09/14/omission [This is a bit long so I copy here the most significant bit for our present purposes: "Writing is selection. Just to start a piece of writing you have to choose one word and only one from more than a million in the language. Now keep going. What is your next word? Your next sentence, paragraph, section, chapter? Your next ball of fact. You select what goes in and you decide what stays out. At base you have only one criterion: If something interests you, it goes in; if not, it stays out. That's a crude way to assess things, but it's all you've got. Forget market research. Never market-research your writing. Write on subjects in which you have enough interest on your own to see you through all the stops, starts, hesitations, and other impediments along the way. Ideally, a piece of writing should grow to whatever length is sustained by its selected material: that much and no more."] >>> another item of possible interest (think of this as a footnote): http://chronicle.com/blogs/linguafranca/2015/09/14/permission-to-footnote ========================================================================== >>>>>> about paper #1 1. This paper is a "major writing assignment" and will be graded (separately) for content and for writing. I will expect a well-written paper of about 6-10 pages (typed). For this purpose, your assumed "audience" consists of people like yourself. Some "rules for good writing": (a) Read. Think. Then have something to say: main points (b) Make sure you understand your own argument and why you believe it (c) Speculation is excellent -- so long as you provide reasoning as to why your speculation is plausible. (d) Care about getting your audience to understand it (e) Be clear. Be concise. (f) Organize the material, write it -- then rewrite it! You are encouraged to discuss this with others, but it is expected to be your own work, with appropriate credit to sources and for quotes or paraphrasing. Use your notes; use the text; use the internet (noting what you are considering trustworthy sources). (g) Then look back, make corrections and rewrite it again. 2. The due date for the paper is Thursday, October 29. If you turn in a fairly final version earlier than that (by at least a week), then I will try to make some editorial comments on both the content and the writing. I will then give an adjusted due date to give you the opportunity for further revision -- but with an absolute deadline before Thanksgiving. 3. The topic is as is indicated above. Note that if you are to understand anything about "how modern math developed to be as it is" then there must be something in the paper about mathematics more recent than the Mesopotamian, Egyptian and Greek developments we have discussed in class so far. 4. Both for content and for writing a large part of the grade will be on the selection of significant points to be made and the cogency/coherence of your arguments used to support these. For writing I then look for organization and appropriate style. I will assume you will have checked for spelling, elementary grammar (case, agreement of number, etc.), suitability for your "assumed audience" (inserting explanation where necessary to make the paper understandable), ... 5. Reread http://userpages.umbc.edu/~seidman/f15/blurb-432.pdf ========================================================================== >>>>>>>> NOTE: The requirement of 12-15 pages given earlier came from a minimum recommendation for the two papers together. What is now the requirement for the first paper is 6-10 (typed) pages. >>>>>>>> https://chroniclevitae.com/news/1150-making-drafts-count >>>>>>>> Even while starting this paper #1 you should already be thinking about paper #2 (for which the topic is up to you, within the scope of the course) -- topic, main points, organization, ... ========================================================================== >>> about Paper#1: I had said that this could be revised after grading for possible grade revision. If you do this, the revision should be turned in no later than Thurs. 11/19 ========================================================================== >>> For Paper#2: [due (FINAL) Tues. 12/1] Thursday 11/24 is the official due date for Paper#2. I have chosen this due date so I can start the grading over Thanksgiving, but will relax the deadline for those who request a bit of extra time. I do remind you that the semester will end fairly soon and that in determining the final grade I will give substantial weight to the summary self-assessment. The subject matter for Paper#2 is some aspect of the concept of "function" in mathematics: variations in the concept and the development of its definition and its role in the development of math as well as the significance of such properties as continuity, etc. You should be making some point and then justifying it. There should be a solid introductory paragraph telling what the paper is `about', followed by the meat of the paper and a paragraph pulling it together (perhaps using concepts which could not have been in the Introduction because they had not yet been introduced). You should provide enough background detail to make your exposition clear to someone (e.g., at the level of this class) who has not read functions.pdf. I expect the use of our text and of functions.pdf as primary references, but encourage the use of some additional sources (e.g., on the web) for additional perspective. I will also be looking at the `English' (appropriate vocabulary, agreement of number, sentence structure, organization into cohesive paragraphs, etc.). Finally, I want to see that the `meat' of the paper shows thinking/understanding and says something nontrivial (your point). [If, as I hope, you find some part of the article particularly interesting, I recommend that you concentrate on that (and add a bit on why you found that interesting).] ========================================================================== ========================================================================== >>>>>> ASSIGNMENTS <<<<<<<< ========================================================================== ========================================================================== >>> The first HW is just a reading assignment from the text: Read Chapter 1 of the text. Be prepared to 1. do exercises 1, 32 (set starting on p.25) 2. compare the two different notations for numbers 3. compare the methods for addition and multiplication of integers 4. discuss how a Mesopotamian multiplication table differs from ours 5. try some problems with Egyptian fractions >>>>>>>>>>>>> Sorry for the delay... =================================================++++===================== >>> HW1 [due in class Tues. 9/8] [numbered HW1 because this is the first to be turned in and graded] 1. compare the ancient Mesopotamian and Egyptian number systems (as described in class and in the text) -- not more than 1 page; to be graded both for content and for "writing" (see */writing-1) 2. do E25/7,8,13,14 =================================================++++===================== >>> HW2 [due Tues. 9/15 -- 1.,2. to be turned in] 1. multiply 509 by 123 (8,29 by 2,03) both by ancient Mespotamian and by ancient Egyptian methods [Hint: use */60mult.pdf] 2. do E25/9 and E62/5 3. read the first 3 topics (Ancient ..) from the link: http://www-history.mcs.st-and.ac.uk/Indexes/HistoryTopics.html 4. prepare for E62/8 [see http://classics.mit.edu/Plato/meno.html --- the geometry dialog from where Meno says, "Come hither, boy," to where Socrates says, "What do you say of him, Meno? ..."] >>> https://www.youtube.com/watch?v=yqDoLdmcyZo >>> */meno.pdf ========================================================================== >>> [due Thursday, 9/17] Turn in a brief (tentative) list of the main points you will want to make for the first major writing assignment --- historical or mathematical. [This is very much a tentative list, just to document that you have started thinking about it, but also already a beginning at organization.] >>> Keep a copy for yourself to start working on the paper. =================================================++++===================== >>> HW3 [due Tues. 9/22] 1. Do E63/6,12 2. Write out a statement and proof of the Pythagorean Theorem 3. Read sections 2.2.2, 2.2.4, 2.2.6 =================================================++++===================== >>> HW4 [due Tues. 9/29 -- turn in 1.,3.] 1. Do E63/13, 14, 20. Explain the discussion (p.56) of Prop. VI-19, etc. 2. Read */Quinn.pdf and the first couple of chapters of */Ruelle.pdf Read Sections 7.2, 9.1, 11.1 (and similar...). [You are only looking for any ideas relevant to your first paper, so just skim the material at this time.] 3. Make an outline for the first paper (and keep a copy for yourself). [You will probably want to discuss this paper with me before investing a lot more work on it.] ========================================================================== >>> HW5 [due Tues. 10/6 -- turn in 3.] 1. Read https://en.wikipedia.org/wiki/Euclid%27s_Elements http://www.pbs.org/wgbh/nova/physics/inside-archimedes-palimpsest.html 2. Watch https://www.youtube.com/watch?v=OGk04igBKhg 3. Write a (half-page?) summary of what you found most interesting here 4. See me to discuss paper #1 ========================================================================== >>> HW6 [due Tues. 10/13 -- turn in 1.,2. ] 1. Read Section 3.3.3 and use this to sketch/explain the specific steps Ptolemy would have needed to construct the first result in Table 3.1 on p.93 (i.e., the chord of 1/2 is 0,31,25 -- be careful to interpret these numbers correctly: e.g., remember that the radius is R=60). 2. Use the web to find 2 modern mathematicians working in areas of modern mathematics which did not exist in classical Greece. Briefly describe what these areas are about. 3. Watch http://www.nytimes.com/2015/07/26/magazine/the-singular-mind-of-terry-tao.html or http://www.smh.com.au/good-weekend/terence-tao-the-mozart-of-maths-20150216-13fwcv.html ========================================================================== >>> HW7 [due Tues. 10/20 -- turn in 1.,2. ] 1. Do E114/1,15 2. Do E134/7,13 (see 5.3.1) 3. Read (in text and online) about Combinatorics and Pascal's Triangle. 4. Watch https://www.youtube.com/watch?v=YaUlqXRPMmY >>> Be prepared to jump forward a thousand years! ========================================================================== >>> HW- [not due Tues. 10/27] >>> Since paper #1 is due on Thur. 10/29, there is no HW due this week ========================================================================== >>> HW- [due Tues. 11/3] >>> Since I did not make any assignment earlier, the only HW due this week is to think about the concept of "an infinitesimal" and its relevance for "the invention of the Calculus" >>> [Extra Credit: write a page on this.] ========================================================================== >>> HW-8 [due Tues. 11/10] >>> Read: http://userpages.umbc.edu/~seidman/f15/functions.pdf >>> Select one (or two) of the subsections (1.--7.) of this to summarize. [This will be for Writing Assignment #2 (due date TBA).] For now, just give a brief outline and an indication of the reason for your choice. ========================================================================== >>> HW-9 [due Tues. 11/17] >>> Find a simple proof on the web of the Schroeder-Berstein Theorem and write it up so you can understand it. ========================================================================== >>> HW-10 [due Tues. 11/24] 1. Explain why the power set of a set S (collection of all subsets) has the same cardinality as the set [all functions from S to the codomain {0,1}]. 2. What is the key role of (some special kinds of) functions to the theory of Linear Algebra? 3. What is the modern view of an "axiomatic system"? (How was this influenced by Non-Euclidean Geometry?) ========================================================================== ==========================================================================