MAT 320 Foundations of Mathematics

(last update 12/15/17, 2:40 pm)

I posted final exam solutions to the BBLearn page. Also please compare your BBLearn grades with your own records to make sure they agree. I hope to finish grading over the weekend and post final grades Monday.

Here are the definitions of maximal and minimal element:

• a maximal element of a subset S of a poset P is an element x of S with the property: if y is in S and x is less than or equal to y, then y=x. Minimal element is defined analogously.
• "bijection" is s synonym for one-to-one correspondence. Such a correspondence between sets X and Y can be expressed as a function from X to Y.

Here is the handout on topological spaces that I handed out along with HW #6:

Finite topological spaces

Reminder to students of the late work policy: if in preparing for the exam you wrote up solutions to exercises or problem sets that you didn't hand in earlier, you can hand them in now (or anytime during the semester) for half credit (e.g., up to 15 points for problem sets). If you want these revised scores to be reflected in your mid-term grade (which I will submit on Friday), please give the work to me by Thursday.

Here is the list of inference rules that I handed out in class. They will be discussed in detail soon:

Inference rules

Syllabus and department policies:

Syllabus (includes tentative exam dates)

Department and University Policies

Link to the BBLearn page (where I post solutions and periodically update the course grades).

BBLearn login page

Problem Sets - see BBLearn page.

Exercises (from Smith, Eggen,St. Andre, A Transition to Advanced Mathematics, 7th edition)

1.1 / 1 (any 4 parts), 2 (any four parts including j), 3b,c,g, 7,9a,c, 10, 11 (any 3 parts)

1.2 / 1c-f, 3, 8a,c,e, 10a,c,h,j, 12a,b,d, 17.

1.3 / 1a,b,e,f, 2a,b,e,f, 3, 6b,c,d, 10,12a.

Exercises from 1.1, 1.2, and 1.3 are due Wednesday 9/6, at the end of class.

1.4 / 5a,c,e,h,6d,7a,k,9a.

1.5 / 1b,3d,10.

1.6 / 1b,e, 2a, 4b,d, 5a, 6i.

Exercises from 1.4, 1.5, and 1.6 are due Monday 9/18, at the end of class.

2.1 / 1a,c, 3,4,5,6,9,13,15,17. (Solutions: 5i, 13)

2.2 / 1b,c,d,h, 2a,d, 3a,e,I, 6d, 10a,c, 11a,c,d, 12, 13b, 14, 15a, 16a,b. (Solutions: 12a, 14, 16a)

Exercises from 2.1 and 2.2 are due Monday 9/25, at the end of class.

2.3 / 1a,c,d,h,6a,8a,10a,12,16.

2.4 / 6a,c, 7a,n, 8a.

Exercises from 2.3 and 2.4 listed above are due Wednesday, 10/4, at the end of class.

2.4 / 1,2,4d,5g,6b,10

2.5 / 1a,,5a,d,6d,8,9.

Exercises from 2.4 and 2.5 listed above are due Wednesday, 10/11, at the end of class.

3.1 / 1,2g,3g,4g,5a,e,g,h,7,8b,9a,c,12

3.2 / 1b,g,i,k,5a-g,8a,c,9c,11,13c

Exercises from 3.1 and 3.2 are due Wednesday 10/18.

3.3 / 2a,b,c,e,3a,d,f,7,8,14.

3.4 / 1a,c,d,g, 2,3b, 5,8,9,14,15. (Solutions: 15)

Exercises from 3.1 and 3.2 are due Monday 11/6.

4.1 / 1a,c,f,g, 4a,e, 5, 6a, 7, 8, 9d, 10, 11a,b,c,f, 18.

4.2 / 1b,j, 3a, 4, 8,9 , 13, 14a,c,e,15 (Solutions : 9, 11, 15)

4.3 / 1a,c,h, 3, 5, 6, 8, 11d.

Exercises from 4.1, 4.2, and 4.3 are due Monday, 11/27.

4.4 / 1a,d, 2b,c, 3b, 5b, 6, 9b,e,f,j.

4.5 / 1,5,7, 8a,b, 9, 10b,c, 12, 13.

5.1 / 3, 4, 11.

5.2 / 3, 7, 8.

5.3 / 2, 7, 12.

5.4 / 3, 5, 10, 14.

5.5 / 7.

Exercises from 4.4, 4.5, and Chapter 5 were not collected or graded.

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