This page is adapted from one that I maintained while at METU. Everything from my old site at METU should be now at my new site at Mimar Sinan; however, most of my pages linked to below will still have links back to my old site at METU. If you want something that should be here and cannot reach it, let me know.
Courses at METU
- 111 (Fundamentals of Mathematics)
- 112 (Discrete Mathematics)
- 115 (Analytic Geometry)
- 116 (Basic Algebraic Structures)
- 119 (Calculus I) (and my few notes)
- 120 (Calculus II) (and my few notes)
- 126 (Basic Mathematics II)
- 219 (Differential Equations)
- 253 (Ordinary Differential Equations)
- 260 (Basic Linear Algebra)
- 271 (Mathematical Analysis I)
- 272 (Mathematical Analysis II)
- 303 (Math history I)
- 304 (Math history II)
- 320 (Set Theory)
- 365 (Elementary Number Theory I)
- 366 (Elementary Number Theory II)
- 368 (Field Extensions and Galois Theory)
- 406 (Mathematical Logic and Model Theory)
- 503 (Algebra I)
- 504 (Algebra II)
- 712 (Set Theory and CH)
- 736 (Model Theory I)
- 746 (Model Theory II)
A (very) few dates in the history of mathematics, from Plato to Descartes.
Some remarks of Gibbon on the usefulness of the education of Emperor Julian (who passed through Ankara on his way to Persia; the so-called Julian's Column in Ankara was supposedly erected in honor of his visit).
Suggestions for (and requests of) students……especially beginning students of mathematics at METU.
Ask yourself: “Why am I at the university?” Two possible answers (perhaps not the only ones) are: “To get a degree” and “To learn.” Family and society may say that a degree is desirable. I think that the degree ought merely to be a sign that learning has taken place; I think that what is truly desirable is the learning itself. There may also be kinds of learning that are not reflected in grades on one's transcript.
University-learning is not the same as what gets you a high score on the university entrance examination. Studying at the dershane may get you into the university; to succeed at the university may require another kind of studying.
The learning that we ask you to do at the university is perhaps not so easy to accomplish unless you want it for itself—unless you are interested in what you are learning. If what you are supposed to learn does not seem interesting, then find a way to make it interesting. (Teachers ought to have some ideas here.)
We ask you to learn to find correct solutions to problems, but also to be able to show why the solutions are correct.
In particular, the work that you give to us teachers will generally be written. So, please write clearly, left to right, top to bottom in the customary fashion. Students sometimes seem to forget this custom on examinations. (Lecturers at the blackboard may also forget this; we shouldn't.) You can't expect to explain to us in person what you have written on an exam; what you write should speak for itself.
Go to class and take notes. This is better than simply studying someone else's notes or a textbook. I still use notes that I took as a student.
As an undergraduate, I was at an unusual college, where the point was to learn from books by discussing them with teachers and classmates; so it would be out of the question not to go to class there. Other universities, like METU, are not the same. Still, you may have more to learn in class here than you realize. See for example some recollections of the logician Alonzo Church by one of his students.
Consider also who will write the exams you take: your teachers, not the textbook-writers, and not writers of past exams (unless they are the same people). So, if only for the sake of your grades, you should know your teachers' approach to the material we teach.
Depending on you and your teacher, it is possible that you can use your time more efficiently than by going to class. In high school, I found one math-class to be too slow, so I stopped attending and spent the time reading ahead in the textbook.
However, if there is something that you don't like about your class, then you should talk to the teacher first before giving up on the lectures.
Learn by doing. Bakmakla öğrenilse, köpekler kasap olurdu [if one learned by watching, then dogs would become butchers]. Just going to class and taking notes is not enough. Memorizing formulas the night before an exam is not enough.
You are in class to learn not the notes, but the mathematics behind the notes. We can't make you learn this; it is up to you. How can you learn? In a word, practice: “the unpractised student will often be perplexed in the application of the most perfect theory”—Edward Gibbon. Here are some specific possibilities:
- Look for different ways to express the contents of your notes.
- Re-do examples from class without looking back.
- Construct new examples.
- Try writing your own exams (this is what your teachers will be doing from time to time).
- Do textbook-exercises of course, but do them in the right way. Learn to do them without referring to similar examples in the text or notes. Learn to recognize kinds of problems without knowing what part of the text they are from.
For more ideas, see:
- “Psychologists' tips on how and how not to learn” by Wilfred Hodges of the School of Mathematical Sciences at Queen Mary, University of London
- Some notes on learning mathematics by Steven Zucker of Johns Hopkins University
It is unfortunate that we teachers must assign grades. In principle, math students can grade themselves, since the standard of correctness is found in all of us: it is reason. A mathematical argument is correct, not because an authority (such as a teacher) says it is correct, and not because some kind of experiment says it is correct, but because your own powers of reason say it is correct. (This is an oversimplification. Math can involve factual questions, concerning definitions, which are established by authorities. Also, math students are sometimes asked to accept, without proof, that certain theorems justifying some techniques are correct. Finally, mathematics may involve applications to the physical world, expressed as word-problems.)
A class without grades is described in Robert Pirsig's book Zen and the Art of Motorcycle Maintenance (this is available in Turkish as Zen ve Motosiklet Bakım Sanatı).
Here is the official grading scheme from the Academic Rules and Regulations at METU:
Teachers may relax these conditions. Here is my view on this practice:
To earn, say, a BB outright in a class, one should earn 80 points in the class. The assignment of scores to students, however, can never be perfect. A student might get 78 points perhaps, when he deserved 81. To avoid this problem, the teacher might give BB to everybody with, say, 75 points. This may give some students a grade higher than they deserve, but it prevents other students from getting a grade lower than they deserve.
In the example, what about the student with 74 points? This student should think that he missed getting a BB by 6 points, not 1.
Moreover, you should not expect any relaxation of the catalogue conditions. Do not try to predict your grade just by comparing your scores to the class average. If most students are getting low scores, then perhaps most students will get low course-grades. Nearly all students here are capable of getting high marks. However, it is not the teachers' job to give you those high marks. It is your job to earn those marks. We are here to help you earn those marks; but you have to take this help during the semester. We cannot “help” you at the end of the semester by giving you points to raise your grade. The end of the semester is too late.