#### Exercise Problems

**Advice for success in the course:** If you are looking for ways to improve your grade then consider the following tips.

**You must be involved in the learning process.**It is not possible to learn mathematics by just going to class and watching the instructor solving problems. You have to work on exercise problems yourself, even if you are not assigned any. You have to study on a regular schedule, not just the night before exams.**You must be involved in the thinking process.**Memorization might be enough to pass a history or a geography course. However, you cannot pass a mathematics course by just memorizing a set of solutions or formulas. You need to understand how to use the ideas yourself.**You must be involved in the writing process.**In a multiple choice exam, it may enough to find the correct answer, even though you don’t have a valid explanation. In a written exam, you need to express the ideas in your mind on a paper by using mathematical symbols together with meaningful sentences, which is exactly why you have taken MATH111 in the first place.

Here is a list of suggested problems from the textbook of the lecture, *Elements of Modern Algebra*, J. Gilbert, L. Gilbert. Seventh edition, several copies of which are available in the reserve section of library.

- Section
**1.4**: 1–6. - Section
**1.6**: 1–4, 9–14. - Section
**2.3**: 1–6, 17–28, 34–40 - Section
**2.4**: 1–12, 17–25. - Section
**2.5**: 1–12, 25–34, 39–42 - Section
**2.6**: 1–12, 16–20 - Section
**3.1**: 15–19, 20, 30, 31, 32. - Section
**3.2**: 4, 9, 10, 13, 14, 15. - Section
**3.3**: 2, 3, 4, 6, 8, 14, 15, 17, 19, 20. - Section
**3.4**: 6, 7, 8, 9, 14, 15, 16, 18, 21, 22, 25, 26, 28, 31, 32, 36. - Section
**3.5**: 1, 2, 6, 7, 15, 18, 20, 34. - Section
**3.6**: 1, 4, 5, 6, 8, 9, 19, 20. - Section
**4.1**: 1 (all), 2 (all), 3, 4, 5, 6, 7, 8, 9, 10, 11. - Section
**4.4**: 1, 2, 3, 4, 16, 18, 21. - Section
**4.5**: 1, 2, 4, 6, 8, 9, 10, 16, 17, 18, 19, 20, 22. - Section
**4.6**: 1, 2, 3, 5, 6, 7, 8, 10, 11, 21, 22. - Section
**5.1**: 1, 2, 3, 4, 7, 19, 21, 27, 28, 29, 36, 37, 38. - Section
**5.2**: 1, 2, 3, 4, 5, 8 (replace the word “assume” with “prove”), 9, 10, 11, 12, 20. - Section
**6.1**: 4, 6, 9, 10, 11, 16, 21, 24. - Section
**6.2**: 6, 8, 9, 13, 14, 15. - Section
**7.1**: 1, 2, 7, 8, 13–20 - Section
**7.2**: 1–12, 19, 20, 21. - Section
**8.1**: 3–9, 11, 12, 13, 17, 18. - Section
**8.2**: 1–17, 23, 25, 29, 34. - Section
**8.3**: 1 (all), 2 (all), 3, 4 (all), 9, 12 (a, b), 13. - Section
**8.4**: 1 (all), 2 (all), 3–17, 20, 21.

Some of the past exam questions can be found below. Keep in mind that we are providing these questions for you to *understand* the solutions, *not memorize*.