This class is cross-listed as:
Euclidean and Transformational Geometry
by Shlomo Libeskind (Jones and Bartlett Publishers, INC 2008)
There are many other excellent introductory geometry books. Reading from other
sources is always very valuable. For example:
Continuous Symmetry. from Euclid to Klein
by William Barker and Roger Howe (American Mathematical Society [AMS] 2007),
or Complex Numbers & Geometry
by UNM Emeritus Professor Liang-shin Hahn (Spectrum Series of the Mathematical
Association of America [MAA] 1994). There are of course the classics, such as
Euclid's Elements which you can find in a very affordable
Dover edition. A personnal favorite is Geometry Revisited by
H. S. M. Coxeter and S. L. Greitzer (The Mathematical Association of America; 1ST edition 1967).
Course Structure: There are 2 lectures per week, Mondays and Wednesdays, that will be devoted to lecturing, solving problems, group work, and student presentations.
Course content: "Geometry" goes back at least four thousand years, the first attempts to formalize it go back more than two thousand years, and a satisfactory understanding of the basic principles behind Euclidean geometry were only understood when mathematicians discovered the non-Euclidean geometries. There is a lot of fascinating history that we will touch, in this journey we are about to embark together. Euclidean geometry is an ideal ground for learning how to think logically, how to deduce results from very basic principles and definitions. It is also a source of fascinating problems that can capture anyones imagination. We will try to exploit the playful side of geometry in the hope that you will be able to enjoy and transmit the beauty and elegance of geometric proofs. We do not expect the students to be able to read, understand, and actually construct mathematical proofs at the begining of the course. A great amount of time will be devoted to learn and practice logical thinking. At the end of the course we expect the students to have adquired the basic skills of mathematical reasoning, and a deeper understanding of geometry.
Group work: We will do group work periodically. The materials we will use for the different activities will be posted here: the proposed activity and any updates and follow-ups from the class discussions. I expect a group report in writing and on the board. Sometimes different groups will tackle different problems, sometimes they will tackle the same problem. In the group report make sure the names of all the members of the group are included, if you have used sources other than the material I have provided, make sure you make proper references (books, online references, etc).
Homework: The problems and exercises in the textbook are an integral part of the course. You should solve as many as possible. Some problems will be attempted working in groups in class. Homework will be assigned periodically, the problems in the homework will be carefully graded, and returned to you with feedback that will help you correct any errors. You are encouraged to discuss the homework with each other, but you should do the writing separately. You learn mathematics by doing, and there is no way around this. It is not enough to see your teacher or your friends solving problems, you have to try it yourself. Difficult as it may seem at the beginning, if you persist you will learn how to write a proper mathematical proof, you will learn how to read and understand other's proofs, and you will learn to appreciate and enjoy the beauty of an elegant argument.
Exams: There will be two midterms during weeks 6 and 12, and a final exam.
Grades: The final grade will be determined by your performance on homeworks, group work, midterms, and a final exam. The grading policies will be discussed in class.
Prerequisites: Math 215 or Math 162 (or permission from the instructor).
Americans with Disabilities Act: Qualified students with disabilities needing appropriate academic adjustments should contact me as soon as possible to ensure your needs are met in a timely manner. Handouts are available in alternative accessible formats upon request.
Return to: Department of Mathematics and Statistics, University of New Mexico
Last updated: Jan 9, 2012