Homework
All assignments, unless otherwise stated, refer to sections in
Number Theory by Andrews.
- For 4/23
- Read and understand Tchebychev's Theorem and the preliminary theorem before it. At least up to claims 8-2-4 and 8-2-5.
- Exercise 1 from Section 8-2.
- For 4/21
- Read and understand Theorems 8-2, 8-3, 8-5 and 8-6
- Exercises 1--10, 15--18 from Section 8-1.
- For 4/16
- Read the rest of Theorem 11-3.
- Exercise 8 from Section 11.2.
- Read and understand Theorems 8-1 and 8-2
- Exercises 1,2,3,4,5 from Section 8-1.
- For 4/14
- Read Theorems 11-2 and 11-3.
- Of the following numbers, say which can and cannot be expressed as the sum of two squares.
Furthermore, express each as a sum of at most four squares:
503, 504, 505, 506, 507, 508, 509.
- For 4/11
- Read Theorems 11-1 and 11-2.
- Pick three numbers between 500 and 600 that can be expressed as a sum of two squares.
- Pick four numbers between 500 and 600 that need at least three squares to be expressed as a sum.
- For 4/9
- Read handout from class on all primes that are 1 mod 4 being representable as the sum of two squares.
- Exam to be given out in class.
- For 4/7
- Read Section 11.1 and all exercises.
- For 4/4
- Read and make notes for Section 9.4. Do all exercises from section.
- Read Section 11.1 and do Exercises 1 and 2 from that section.
- For 4/2
- Read and make notes for Section 9.3. Do exercises 4,5,6 and 7.
- We will read the proof of The Quadratic Residue Theorem together in class. Please read that especially carefully.
- For 3/31
- Don't forget to bring take home quiz to class. Available outside of Roop 323.
- Read and do all questions from Sections 9.1 and 9.2.
- Read and make notes for Section 9.3.
- For 3/26
- See Reading Guide again. All questions due for Wednesday.
- Read and do all question from Section 9.1
- For 3/23
- For 3/19
- Bring take home test to class at start of class.
- Read 5.4. Record definitions and examples in journal.
- Problems from 5.4: 1,3,4,5,7,8.
- For 3/17
- Yet again, another snow day. Again.
- For 3/7
- Read 5.3 and 5.4. Record definitions and examples in journal.
- Problems from 5.3: 1(a,b,c only), 2,4,5,6.
- Problems from 5.4: 1,3,4,5,7,8.
- There will be a take home test on Chapters 3, 4 and 5 handed out in class. Due for Monday 3/17.
- For 3/3
- For 2/28
- Problems from 5.2: 13,14,16--20, 23.
- [Class on Friday will be a problem day on 5.2.]
- For 2/26
- Read 5.2. Record definitions and examples in journal.
- Problems from 5.2: 1--8. (For 3, recall Theorem 1-2 on Page 5)
- For 2/24
- Read 4.2 and 5.1 again. Record definitions and examples in journal.
- Problems from 4.2: 1--4 (again).
- Problems from 5.1: 1(give one solution only), 2(try to find a solution - can you
guess when a solution can be found and when it cannot?), 3 (see definition 5-2).
- For 2/21
- Read 4.3 and 5.1. Record definitions and examples in journal.
- Problems from 4.2: 1--4.
- Problems from 4.3: 1 and 2.
- For 2/19
- Read 4.2. Record definitions and examples in journal.
- Problems from 4.1: 1--7.
- For 2/17
- Read 4.1. Record definitions and examples in journal.
- Problems from 3.4: 1,2,4,5,6,8.
- For 2/14
- For 2/12
- Read 3.4. Record definitions and examples in journal.
- Problems from 3.3: 1 and 2.
- For 2/10
- For 2/7
- Read 3.3. Record definitions and examples in journal.
- Problems from 3.2: 1--6 inclusive.
- For 2/5
- Read 3.1 and 3.2. Record definitions and examples in journal.
- Problems from 3.1: 1,2,3,7,8,9,10,11.
- For 1/31
- There will be a short in-class test on Chapters 1 and 2.
- Problems from 2.4: 1,2,5,6(a,b only),7,8,9(a,b only),10,11.
- For 1/29
- Read 2.4. Record definitions and examples in journal.
- Problems from 2.3: 1(a, b only),2,3(a,b only),4,5,6.
- For 1/27
- Read remainder of 2.2 and read all of 2.3. Record definitions and examples in journal.
- Problems from 2.2: 2, 3, 4, 5(a and b only),8, 10.
- For 1/24
- Read 2.2, pages 15,16,17. Record definitions and examples in journal.
- Problems from 2.2: all parts of 1.
- For 1/22
- Read 2.2. Record definitions and examples from these sections in journal.
- Problems from 2.1: 1-7. Hints for 1 and 6 are in back of text.
The ideals of 4 and 5 generalize considerably in algebra.
- For 1/17
- Again, see Page 3 of Syllabus and begin computational problems on Pages 47-48 of text.
These fourteen problems are due for Tuesday 1/21. Each group of three should take two problems each..
- Read 2.1. Record definitions and examples from these sections in journal.
- Problems from 1.2: 1,2,3,5. (You need only understand the statement of Theorem 1-3 for the exercises, not its proof.
In 5, replace 80 by 40.)
- For 1/15
- Purchase a hardback journal, distinct from the notebook within which you take class notes.
- Read Syllabus in full.
- See Page 3 of Syllabus and begin computational problems on Pages 47-48 of text. These fourteen problems are due for Tuesday 1/21.
- Read 1.1 and 1.2. Record definitions and examples from these sections in journal.
- Problems from 1.1: 1,2,5,6,7,9,11,12, 14,17,18. (you are allowed to use earlier problems to solve latter ones).