MATH 3GR3 Final Exam Information

• The final exam will be held from 7:30pm to 10:00pm ET on Tuesday, 12 December.
  
• Check on Mosaic to find the location of the exam.
  
• Make sure that you bring your McMaster student card with you to the exam.
  
• No aids will be allowed during the exam, including calculators.
• The exam will consist of a number of True/False questions and full-answer questions, similar in style to the midterm test questions.
  
• In your solutions, you may not use any theorems or results that have not been covered in the lectures.  So, you may not use any theorems that are usually presented in more advanced courses, such as MATH 4GR3.
  
• To prepare for the exam, you should look over the relevant sections of the textbook, review your lecture notes, and go over the assignment and midterm tests questions and solutions.  In addition, you should try to do a good number of questions from the end of each of the chapters of the text that have been covered in the course.
• Make sure that you are familiar with the various examples of groups and rings that have been discussed in the course.  You should be familiar with the notation that has been set up to refer to certain groups and rings.  For example, U(n) refers to the group of units modulo n (you should know what this group is).
• You should know the definitions of the concepts introduced in the course, along with the statements and proofs of the theorems, lemmas, and corollaries covered.  You can expect to be asked to provide details of at least one of the theorems covered in the lectures.
  
• The exam will cover material from the course up to and including the material found in Section 17.2 of the course textbook.
  
• Specifically, it will cover material from the following sections:  1.2 (Equivalence Relations and Partitions), 2.2, 3.1, 3.2, 3.3,  4.1, 5.1, 5.2, 6.1, 6.2, 6.3, 9.1, 9.2, 10.1, 11.1, 11.2, 16.1, 16.2, 16.3, 16.4, 17.1, 17.2 (just up to and including Corollary 17.9). You should also be familiar with the basic properties of the integers found in Chapter 2.  You will not be tested on anything to do with the SageMath system.  You will also not be tested on the proof of Lemma 5.14 or on the simplicity of the groups A_n for n > 4.
• A copy of a recent MATH 3GR3 exam can be found here (solutions).  Note that this exam was conducted via zoom (during the pandemic) and so the types of questions and the format of this exam are non-standard. The duration of the sample exam was 100 minutes.
  
• Here are some additional questions from the end of some of the chapters of the text that can be used to prepare for the final exam.  These are in addition to the supplemental problems provided in the assignments this semester.
• Chapter 3: 31, 37, 41, 47, 48, 51, 53
• Chapter 4: 5, 11, 13, 27, 28, 31, 33
• Chapter 5: 2, 7, 10, 11, 18, 27, 34, 36
• Chapter 6: 1, 2, 6, 9, 18, 19
• Chapter 9: 1, 2, 3, 8, 18, 20, 21, 24, 25, 28, 32, 47
• Chapter 10: 7, 8, 10, 11
• Chapter 11: 11, 14, 17, 19
• Chapter 16: 3, 4, 9, 27, 31, 37
• Chapter 17: 7, 12, 17, 19, 28
• Leading up to the exam, Dr. Valeriote will hold office hours from 9:00am to 10:00am (NOTE:  the time for this office hour has changed) 10:00am to 11:30am on Friday December 8,  from 1:30pm to 3:00pm on Monday December 11, and  from 10:00am to 11:30am on Tuesday, December 12.He will also be available by appointment and by email. 
• The course TA Mike will hold office hours on December 12, from 12:30 to 1:30pm in Hamilton Hall Room 312.