MATH 116
BASIC ALGEBRAIC STRUCTURES
Spring 2007-2008
THIS PAGE IS UPDATED EVERY WEEK, !!
Please check your METU e-mail and the Web page of the course, at http://www.math.metu.edu.tr/~semra/116, at least once a week for massages/updates.
METU-Online will be used as well: https://online.metu.edu.tr/
Section 1 : Mohan Bhupal, Office Hr. M 238, e-mail bhupal followed by metu.edu.tr
Section 2, 3: Semra Kaptanoğlu, Office Hr. M 138, sozkap followed by metu.edu.tr There is a student assistant for the course , Özhan Genç, he wıll have offıce hours.!!
A VERY NICE "PROBLEM BOOK WITHH SOLUTIONS CAN BE REACHED FROM here .
*The grades over 80 from Make-Up exam are normalized to 60 for midterms.
MAKE -UP EXAM WILL BE ON JUNE 12, at 9:30 in M 231
NEW !! For students who will be taking the MAKE-UP EXAM should write their name, and the exam missed and the reason for missing the exam on a paper and give it to me after the final exam.
FINAL EXAM WILL BE IN THE FOLLOWING ROOMS in the MATHEAMTICS BUILDING.
| Last name | Room |
| Abdullayev-Ay | M 102 |
| Ayan-- Çabuk | M 103 |
| Çakıroglu--Durraj | M 104 |
| Durşen--Güzelsu | M 105 |
| Hasanoğlu--Koyuncu | M 106 |
| Kurbal--Tufan | M 05 |
| Türker--Özeğdemir | M 06 |
| Özkan--Tunç | M 07 |
| Turan--Zeray | M 08 |
(8.4 is a required reading for the course, it is not going to be in the final exam)
EXAM 2 GRADES are here. Solutions are here.
You can see your Exam 1 and 2 papers during the office hours of Semra Kaptanoglu, between May 20 and May 30th, Monday and Wednesday 9:40--11:30 in M 138.
EXAM 2 will cover the material covered in class from 3.4 , 3.5, 4.1, 4.2, 4.4, 4.5, 5.1
The first exam will test you from the beginning to the end of chapter 3 of the textbook (the sections skipped are not included).
EXAM 1 solutions are here, page1 , page 2.
# The fourth set of solutions to some of the selected exercises are here
# The third set of solutions to some of the selected exercises are here page 1** , page 2
** WARNING THERE IS A MISTAKE IN THE SOLUTION of 2.5.22, a correct solution for 2.5.22, and a BETTER SOLUTION TO 2.6.20 are here ,
#The second set of solutions to some of the selected exercises are here, page 1* , page 2 , pages 3-4-5* Here are shorter solutions to #9, and #19 of section 2.4 .
# The first set of solutions to some of the selected exercises are here, pages 1-2, pages 3-4 , page 5.
Schedule for lectures and office hours
| Time + 50 minutes | Monday |
Tuesday | Wed. |
Thursday |
Fri. |
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| 8:40 |
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| 9:40 | Office Hr. M138 |
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Office Hr. M 138 |
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| 10:40 | Office Hr. M 138 |
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Office Hr. M 138 |
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| 11:40 | Math 116 Sec. 1 EA 201 | ||||
| 12:40 | Math 116 Sec. 2 EA 208 |
Math 116 Sec.3 EA 201 |
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| 13:40 | Math 116 Sec. 3 EA 208 |
Office Hr. M 238 | Math 116 Sec 1 EA 201, Sec. 2 EA 211 |
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Office Hr. M 201 Özhan Genç |
| 14:40 | Math 116 Sec. 3 EA 208 |
Office Hr. M 238 | Math 116 Sec.1 EA 201, Sec.2 EA 211 |
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Office Hr. M 201 Özhan Genç |
| 15:40 |
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| 16:40 |
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Textbook: Elements of Modern Algebra, J.Gilbert and L.Gilbert, Brooks/Cole,2000, 5th Edition.
There are four copies of the textbook in the RESERVE Room of the METU Library
Exams and Grading: There will be two midterms and a final.
Midterms will be 30 % each, and final will be 40 % of the grade.
There will be only one make-up after the final exam. To be able to take the make-up your excuse should be approved by your instructor otherwise you cannot take that exam.
The make-up will cover all the topics and it is harder than the usual exams.
Selected exercises : There will be selected exercises from each section covered ( see the last column of the Course Outline below).
Definitely these are not sufficient to learn the material, you should do more exercises.
Solutions to some of them will be posted on the web page. There will be no grading for them.
The key for success is to S T U D Y R E G U L A R L Y: One good way to study for the course is to read the topics to be covered before coming to the class. Do the relevant exercises of the section covered right after the classs, at least before coming to the next class. Most of the students took Math 111 last semester from Semra Kaptanoğlu. If you are not one of them, make a quick review of Math 111. In particular, I suggest them to read the section 2.6 titled Writing Mathematics from the book Proofs and Fundamentals by Ethan D. Bloch ( it should be in the RESERVE Room of the Library.)
You should study regularly starting from the first day. If you do this you will not need to study for the exams. It is a very bad strategy to skip classes to study for the nearest exam!
Wk |
Dates |
Sections to be covered |
Selected Exercises |
| 1 | Feb. 18-22 | 1.4 Binary Operations | From 1.4 .#'s 1 b, d , 2 b, c ,f, 3, 10 b, i, n , 11 b, i , n , 13, 14, 19 |
| 2 | Feb. 25-29 | 1.5 Matrices |
From 1.5.#'s 1 e, 2 b, 3 a , j , 8, 9, 10 , 11, 12, 25, 26 Encouraged reading before 2.3 starts is 2.1,and 2.2 |
| 3 | Mar. 3-7 | 2.3 Disibility 2.4 Prime factors and Greatest Common Divisor |
From 2.3. #'s 8,16,20, 21, 22, 28, 30 From 2.4. #'s 3 m, 9, 19, 20, 21, 27 |
| 4 | Mar.10-14 | 2.5 Congruence of Integers 2.6 Congruence Classes |
From 2.5 #'s 14, 22, 23(a), 28, 29, 30, 38. From 2.6 #'s 5(c), 8(b), 8(h), 12, 16, 20 |
| 5 | Mar.17-21 | 3.1 Definition of a Group 3.2 Subgroups |
From 3.1 #'s 5,6,14,17,22,28,32,35,47,51 From 3.2 #'s 3,6,10,11,13,d,17,18,23,27,35 |
| 6 | Mar.24-28 | 3.3 Cyclic Groups | From 3.3 #'s 2,3,6,7 a,b,d, 8 a,b,d, 12, 14,19, 21,22,24,27,30 |
| 7 | Mar.31-Apr.4 | 3.4 Isomorphisms 3.5 Homomorphisms |
From 3.4 #'s 1,2,3,4,6,7,13,14,16,20,22,23,26 From 3.5 #'s 2, 9, 13, 15 |
| 8 | Apr.7--11 | 4.1 Finite Permutation Groups
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From 4.1 #'s 1 a, h, 2 b, d, 3 a, h, 4 b, d , 5, 6, 9 a, f, 10 b, d, 14, 15
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| 9 | Apr.14--18 | 4.2 Cayley's Theorem First Midterm on Apr.18, Friday 17:40 |
From 4.2 #'s 1, 3, 4, 5 , 6 |
| 10 | Apr.21--25 | 4.4 Normal Subgroups No classes on Wednesday, 23 Nisan Çocuk Bayrami |
From 4.4 #'s 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15 16, 19, 20, 21, 25, 26, 27, 30, 31, 32, 34, 38 |
| 11 | Apr.28--May 2 | 4.5 Quotient Groups 5.1 Definition of a Ring
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From 4.5 #'s 1, 2, 3 , 9a, 10, 11, 15, 16, 26 From 5.1 #'s 1a, 4 , 5, 7e, 8e, 9, 14, 16, 17, 19, 20, 21, 22, 23, 25, 26, 29, 31, 38, 40 |
| 12 | May 5--9 | 5.2 Integral Domains and Fields 6.1 Ideals and Quotient Rings Definition of ring isomorphism (from 6.2.) Second Midterm on May 9, Friday 17:40 |
From 5.2 #'s 2,5,6, 7, 8,10, 18, 19 From 6.1 #'s 1--11, 13,14,15,18,20--24 From 6.2 #'s 7,8,10,15
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| 13 | May 12--16 | 8.1 Polynomials over a Ring |
From 8.1 #'s 1,2,3,5,7,8,9,11,17 |
| 14 | May 19--23 | No classes on Monday, 19 Mayis Genclik ve Spor Bayrami 8.2 Divisibility and Greatest Common Divisor |
From 8.2 #'s 3,5,7,9,11,13,15,16,21 |
| 15 | May 26--30 | 8.3 Factorization in F[x] 8.4 Zeroes of a Polynomial (time permitting?) |
From 8.3 #'s 1--3, 7--12, 14 (8.4 is a required reading for the course, it is not going to be in the final exam) |
| FINAL EXAM is on JUNE 9 |