Algebra is the study of operations, rules and procedures to solve equations. The origin of the term 'Algebra' seems to go back to a IX Century treaty by an Arab mathematician with the title 'The Compendious Book on Calculation by al-jabr and al-muqabala'. The term

Algebra is one of the pillars of Mathematics and this course gives an introduction to the basics of Algebra, including conceptual proofs of all main results.

- Announcements
- Syllabus
- Textbooks
- Grading Policy and Exams
- Homework Assignments
- Emergency information for students in Mathematics courses

- You can find the grades of the final exam on-line. A graph with the grades of the final is available here. Note that the grades of the best 10 homeworks, midterms and final exam is an integer less or equal to 100. Your total score (TS) for the course is obtained by the formula 1.5*HW+MT1+MT2+MT3+3*FE (maximum 750), so that homework is worth 20%, midterms 40% and final exam 40%. Your final grade is obtained from the total score by applying the following curve:
- A+: TS>=740
- A: 740>TS>=715
- A-: 715>TS>=700
- B+: 700>TS>=660
- B: 660>TS>=600
- C+: 600>TS>=550
- C: 550>TS>=500

- Here is a solution of the final exam.
- The last day of instruction for this class is Friday, Dec. 6.
**Important annoucements**:- There will be no office hours the week Dec 9-13. I will be available all afternoon in my office on Tuesday (Dec 17) and Wednesday (Dec 18), the days before the final.
- The final will be held on Thursday, Dec 19, at 1.30 pm, in the regular classroom. I have made available a mock Final to practice.
- The final grades will be available on this web page on Friday, Dec 19, by noon.
- Students can consult their final in my office on Friday, Dec 19, at 2 pm. After that all grades will become final and cannot be changed.

- Students can view the scores of homework on-line (please note that you will have to log in).
- Here is a solution of 3rd Midterm and you can find your score here. I will not curve the midterm, but you can see how you did relative to your classmates in this plot of 3rd midterm grades.
- Here is a solution of 2nd Midterm and you can find your score here. I will not curve the midterm, but you can see how you did relative to your classmates in this plot of 2nd midterm grades.
- The drop deadline for this course is November 15, 2019. Please see this leaflet for information about droping this course.
- Here is a solution of 1st Midterm and you can find your score here. I will not curve the midterm, but you can see how you did relative to your classmates in this plot of 1st midterm grades.

- Chapters 1-6 of the recommended text, covering: Fundamental theorem of arithmetic, congruences. Permutations. Groups and subgroups, homomorphisms. Group actions with applications. Polynomials. Rings, subrings, and ideals. Integral domains and fields. Roots of polynomials. Maximal ideals, construction of fields.
- Frederick M. Goodman,
(Edition 2.6), SemiSimple Press Iowa City, IA. [**Algebra: Abstract and Concrete**`PDF file available for download free of charge`] - Manuel Ricou and Rui L. Fernandes,
[**Introduction to Algebra**`these are my notes that cover the same material but in different order; may contain typos`] - Michael Artin,
, (2nd edition) Prentice Hall, 1991. [*Algebra*`some level as the recommended textbook with alternative approaches`] - Garrett Birkhoff and Saunders MacLane,
, (4th Edition), Macmillan, 1977. [*A survey of modern algebra*`a classic book; more advanced than the recommended textbook`] **Homework and quizzes (20% of the grade)**: Homework problems are to be assigned once a week. They are due the following week, at the beginning of the Monday class.**No late homework will be accepted.**There will be 13 homework assignments, but only the ten best grades will count and the other homework grades will be dropped. If necessary, quizzes may be offered during the semester.**Midterms (40% of the grade):**The midterms will take place in class on Friday Sep 20, Friday Oct 18 and Friday Nov 15 (the dates are subject to change).**Final Exam (40% of the grade):**You have to pass the final to pass the course. According to the non-combined final examination schedule it will take place Thursday, Dec 19, 1.30 pm, in the regular classroom.-
**Homework #1:**Goodman, Exercises 1.3.1, 1.3.2, 1.3.3, 1.4.1, 1.4.2, 1.4.3, 1.5.1, 1.5.2, 1.5.3. [`Important Note: In the textbook, the only symmetries considered are rigid motions, i.e., rotations+translations`]. -
**Homework #2:**Goodman, Exercises 1.5.5, 1.5.6, 1.5.8, 1.5.9, 1.5.10, 1.7.4, 1.7.5, 1.7.6, 1.7.8, 1.7.9. -
**Homework #3:**Goodman, Exercises 1.6.3, 1.6.4, 1.6.7, 1.6.8, 1.6.9, 1.10.1, 1.10.2, 1.10.3, 1.10.4. -
**Homework #4:**Goodman, Exercises 1.10.5, 1.10.6, 2.1.2, 2.1.4, 2.1.5, 2.1.6, 2.1.7. -
**Mock midterm 1**to practice. -
**Homework #5:**Goodman, Exercises 2.1.10, 2.1.11, 2.1.12, 2.2.2, 2.2.4, 2.2.6, 2.2.9, 2.2.11. -
**Homework #6:**Goodman, Exercises 2.2.14, 2.2.15, 2.2.16, 2.2.17, 2.2.19, 2.3.5, 2.3.7, 2.3.8, 2.4.5, 2.4.8, 2.4.9. **Homework #7:**Goodman, Exercises 2.4.13, 2.4.17, 2.4.18, 2.5.4, 2.5.6, 2.5.7, 2.5.8, 2.5.13, 2.5.14, 2.6.1, 2.6.3, 2.6.5.**Homework #8:**Goodman, Exercises 2.6.6, 2.7.3, 2.7.4, 2.7.6, 2.7.7, 3.1.9, 3.1.10, 3.1.13.-
**Mock midterm 2**to practice. **Homework #9:**Goodman, Exercises 5.1.3, 5.1.5, 5.1.7, 5.1.8, 5.1.9, 5.1.12, 5.1.13, 5.1.14, 5.1.15.**Homework #10:**Goodman, Exercises 5.2.2, 5.2.4, 6.1.1, 6.1.4, 6.1.6, 6.1.10, 6.1.11, 6.2.1, 6.2.3, 6.2.4.**Homework #11:**Goodman, Exercises 6.2.7, 6.2.8, 6.2.9, 6.2.10, 6.2.11, 6.2.16, 6.2.19, 6.3.2, 6.3.7, 6.3.8.**Homework #12:**Goodman, Exercises 6.3.1, 6.3.3, 6.3.5, 6.3.6, 6.3.9, 6.3.10, 6.3.11.-
**Mock midterm 3**to practice. **Homework #13:**Goodman, Exercises 6.4.1, 6.4.4, 6.4.7, 6.4.8, 6.4.13, 6.4.14, 6.4.16, 1.8.6, 1.8.7, 1.8.10.-
**Mock Final**to practice. - How many homework assignments will there be? At least 12, but eventually there will be more, depending on the weeks when there are midterms.
- How is the grades of the homework calculated? Only the ten highest grades will count for your total homework grade. The homework grade will be the average of the ten best grades.
- How is each homework assignment graded? Each homework assignment receives a grade in the range 0-10 (0 minimum, 10 maximum). The grader will only grade 3 or 4 problems from each homework set (the same problems for all students).
- Can I turn in late homework? No.
- Can I turn in homework via e-mail? No.
- What if I fall sick, or what if I decide to go to Las Vegas to get married, or... , and I cannot turn in homework on time? One of the reasons that only the 10 best grades will count is to accommodate for such situations.

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