5-5080, atma “at” math here at umd dot edu
Office Hours: MW 11:30-noon or by appointment
Class meets Mondays and Wednesdays 10:00am-11:30am in Math 1311.
Course page: http://www.math.umd.edu/~atma/hp07.htm (or on Blackboard)
Course description: The aim of this course is to introduce students to the interactions, interrelations, and analogies between mathematics and art.
Mathematicians (and scientists, in general) are in search of ideas, truth and beauty, not too different from artists. Our task will be to see the parallels between the viewpoints, the inspirations, the goals of (and the works produced by) artists and scientists.
We shall begin with examples from history of art (such as the theory of perspective due to Leonardo da Vinci), works of art (such as Durer's Melancholia, Escher’s Waterfall), architecture (Parthenon, Le Corbusier) to illustrate the impact of mathematics on art. Of special interest to us will be the period of the Italian Renaissance and also the early part of the 20th century (the new viewpoint on space-time). Time permitting, the affinity of music with mathematics will also be explored (as in the music of Bach, or the foundations of tone, the role of harmony). Simultaneously, we shall explore beauty in mathematics; this will be amply illustrated with examples from the history of mathematics. Emphasis will be put on the aesthetic aspect of things. We will even see how truth and beauty come together in a beautiful proof.
The course material could be roughly divided into three parts: geometry and classical art, truth and beauty in math (proofs), beauty in science (higher-dimensions, space-time, physics) and modern art (Cezanne, Picasso, Escher, Kandinsky).
All through the semester, we will be comparing and contrasting the two subjects. Hopefully, by the end of the semester, one's sense of beauty will be enriched also to appreciate beauty in the world of mathematics.
Books: (Additional reading material will be distributed via Blackboard)
Jinny Beyer, Designing tessellations
Amir Aczel, The artist and the mathematician
Hans Magnus Enzenberger, Number Devil
William Ivins, Art and Geometry: Study in space intuitions
Mario Livio, The equation that could not be solved: How mathematical genius discovered the language of symmetry
Tor Norretranders, The user illusion
Leonard Shlain, Art and Physics
Leonard Shlain, The alphabet versus the Goddess: The conflict between Word and Image
Theodore Cook, The curves of life
Arthur Loeb, Concepts and Images: Visual Mathematics
Samuel Colman, Harmonic proportions and Form in Nature, Art and Architecture
George Gamow, The new world of Mr. Tompkins (revised and updated)
Howard Gardner, Creating Minds: An anatomy of creativity seen through the lives of Freud, Einstein, Picasso, Stravinsky, Eliot, Graham and Gandhi
H. E. Huntley, The Divine Proportion
Hermann Weyl, Symmetry
Georges Ghevergese Joseph, The crest of the Peacock
Daniel Pedoe, Mathematics and the visual Arts
Douglas Hofstadter, Godel, Escher and Bach.
Robert Pirsig, Zen and the art of motorcycle maintenance.
Jerry King, The art of mathematics.
Walter Pater, The renaissance.
Subrahmanyam Chandrasekhar, Truth and Beauty.
V. S. Ramachandran, Shadows in the Brain
Roger Penrose, The emperor’s new mind and Shadows of the mind: a search for the missing science of consciousness
C. P. Snow, The two cultures
Carol Parikh, The unreal life of Oscar Zariski
Barbara Goldsmith, Obsessive Genius: The inner life of Marie Curie
Rebecca Goldstein, Incompleteness: The proof and paradox of Kurt Godel
Albert Einstein, Ideas and Opinions
Paul Hoffman, The man who loved only numbers: The story of Paul Erdos and the search for mathematical truth.
Robert Kanigel, The man who knew infinity
Andre Weil, The apprenticeship of a mathematician
Maurice Mashaal, Bourbaki: a secret society of mathematicians
Hilbert and Vohn-Cossen, Geometry and the imagination
Jacques Hadamard, The psychology of invention in the mathematical field
Rene Descartes, Discourse on method and meditations on first philosophy
Johannes Kepler, The harmony of the world
Keith Devlin, Mathematics: the science of patterns.
Bulent Atalay, Math and the Mona Lisa: The art and science of Leonardo da Vinci.
Arthur Miller, Einstein, Picasso: Space, Time, and the beauty that causes havoc.
(There is so much material available in books (go to the Popular Math section of your favourite bookstore) and online that it is impossible to list. I urge you to google ``Math and Art''.)
Plays: Tom Stoppard,
Tom Stoppard, Rosencrantz and Guildenstern are dead.
Joanne Sydney and Joshua Rosenblum, Fermat’s Last Tango.
Useful periodicals: American Mathematical Monthly, The Mathematical Intelligencer, Mathematics Magazine, Scientific American,.
Course Format and Grading:
This is a seminar. As such, there will be both lectures and discussions. Students are expected to actively participate in class. There will be reading assignments and students are supposed to come prepared to discuss them in class. There is an overabundance of reference material (see course homepage). In-class and out-of-class discussions are greatly encouraged. There will be guest lectures and (perhaps) a field trip to a museum in DC.
Discussions and Class participation
Many topics are possible for the final paper; here are -- but only a few -- suggestions: From "Leonardo da Vinci, the Renaissance human" to "The mathematics of snowflakes" to "How did Escher make his drawings" to "Why the second law of thermodynamics is beautiful" to "Comparison between the works of Newton, Shakespeare and Beethoven". It is best to choose a topic that is close to your actual interests.
Class on 19th November will be devoted to a discussion of Final Paper/Project.
Students will obtain constructive suggestions and criticism from instructor and classmates.
Other academic matters:
• Academic Accommodations: If you have a documented disability,
you should contact Disability Support Services 0126 Shoemaker Hall. Each
semester students with documented disabilities should apply to DSS for
accommodation request forms which you can provide to your professors as proof
of your eligibility for accommodations. The rules for eligibility and the
types of accommodations a student may request can be reviewed on the DSS web
site at http://www.counseling.umd.edu/DSS/receiving_serv.html.
• Religious Observances: The University System of Maryland policy provides that students should not be penalized because of observances of their religious beliefs, students shall be given an opportunity, whenever feasible, to make up within a reasonable time any academic assignment that is missed due to individual participation in religious observances. It is the responsibility of the student to inform the instructor of any intended absences for religious observances in advance. Notice should be provided as soon as possible but no later than the end of the schedule adjustment period. Faculty should further remind students that prior notification is especially important in connection with final exams, since failure to reschedule a final exam before the conclusion of the final examination period may result in loss of credits during the semester. The problem is especially likely to arise when final exams are scheduled on Saturdays.
• Academic integrity: The
is one of a small number of universities with a student-administered Honors Code Universityof Maryland
and an Honors Pledge, available on the web
The code prohibits students from cheating on exams, plagiarizing papers, submitting the same paper for credit in
two courses without authorization, buying papers, submitting fraudulent documents, and forging signatures.
The University Senate encourages instructors to ask students to write the following signed statement
on each examination or assignment:
"I pledge on my honor that I have not given or received any unauthorized assistance on this examination (or assignment).”
In the event of inclement weather or other emergencies affecting the campus area,
classes and exams will be held unless the campus is officially closed.
You can check the campus web page or call 301-405-SNOW for snow closure information.
Should any classes or exams be cancelled, please check the class schedule page
for updated schedule information.
Please keep visiting the course page (and/or Blackboard) for updates.
This course is part of CORE Distributive Studies: CORE: Mathematics and Sciences, non-lab [MS].
Students should be able to: