This is the Web Page for the course 3010334 Foundations of Mathematics.

1. Due to the special circumstances of the covid-19 pandemic, the course will hold some few online lectures in Spanish, but most of the work will be based on students' autodidact work.

2. The official textbook (Proofs and Fundamentals by Ethan Bloch) is in English as well as all the other bibliographic references. Therefore, an important portion of the written work will run in English as this web page.

Here you will find:

1. Syllabus 3010334.

2. Schedule of Activities.

3. An update of the course content covered on a session-by-session basis.

4. Textbook and Reading Materials.

5. Homework Assignments.

6. Test Dates and Solutions.

7. Links to online Free Courses Related to Foundations of Mathematics.

8. Inspirational and Confusing unrelated material intended to push out-of-the-box thinking and free association of ideas.

This is the list of references to be used in order of priority.

1. Proofs and Fundamentals. Ethan Bloch. (Freely available for UNAL students)

2. Introduction to Mathematical Structures and Proofs. Larry J. Gerstein. (Freely available for UNAL students.)

3. A Logical Introduction to Proof. Daniel W. Cunningham. (Freely available for UNAL students.)

4. The Foundations of Mathematics. Thomas Q. Sibley.

5. Discrete Mathematics and Applications. Susanna Epp.

1. Class 1

2. Class 2

3. Class 3

4. Class 4

5. Classes 5 and 6

6. Class 7

7. Class 8

8. Class 9

9. Class 10

10. Class 11

11. Class 12

12. Class 13

13. Class 14

14. Class 15

15. Class 16

16. Class 17

17. Class 18

18. Class 19

19. Class 20

20. Class 21

1. August 6th, 2020. Presentation of the course, evaluation method and dynamics of the course. Problem set 1 avaiable here.

2. August 11th, 2020. List of sections for TUTORIAL activities available. Read sections 1.1 and 1.2 from Reference 1. Support slides for the first class available here. Suggested problems: 1.1, 1.10, 1.11, 1.12, from Problem set 1. Find here a TED talk given by Sal Khan, the founder of Khan Academy on how to use virtuality to revolutionize education which perfectly applies to our current pandemic conditions

3. August 12th, 2020. Read section 1.2 and section 1.3 until the first paragraph of page 16. Support slides for the second class available here. Suggested problems: 1.2, 1.14, 1.15, from Problem set 1.

4. August 13th, 2020. Read section 1.5, Support slides for the third class available here. Suggested problems 1.3, 1.4, 1.5, 1.6, 1.17, 1.7, 1.8, 1.9 from Problem set 1.

5. August 18th, 2020. Read section 8.2 from Reference 1 and sections 6.3, 6.4 from Reference 2. Support slides for the fourth class available here. Suggested problems: 2.2, 2.3, 2.4 and 2.5 (very important for Computer Scinece majors) from Problem set 1.

6. August 19th, 2020. Read section 2.1, 2. 2, 2.3 until the first paragraph of page 16. Support slides for the fifth class available here. Suggested problems: 1.18, 1.22, 1.26, 1.30, 2.2, 2.3 from Problem set 1.

7. August 20th, 2020. Read section 2.4, 2.5, 2.6, Support slides for the sixth class available here. Suggested problems 3.18, 4.3, 4.8, 3.1, 3.3, 3.7, 3.9 from Problem set 1.

8. August 25th, 2020. Problem set 2 available here. Read section 4.3 from Reference 3. Support slides for the seventh class available here. Suggested problems: 1.1 , 1.2, ..., 1.10 from Problem set 2. Find here a Coursera course on Mathematical Thinking for Computer Science (extremely useful for CS mayors in the class). It is a beginners level course.

9. August 26th, 2020. Read sections 4.3, 4.4 from Reference 3. Support slides for the eighth class available here. Suggested problems: 2.1, 2.3, 2.5, 2.7, 2.8, 2.9, 2.10, 2.11, 2.12, 2.18, 2.19 from Problem set 2.

10. August 27th, 2020. Read sections 4.5, 4.6 and 4.7 from Reference 3, Support slides for the ninth class available here. Suggested problems 2.14, 2.15, 2.16, 2.17, 2.20, 2.25 from Problem set 2.

11. September the 1st, 2020. Problem set 2 available here. Read sections 3.1, 3.2 from Reference 1. Support slides for the 10th class available here. Suggested problems: 1.1 , 1.2 1.4 and 1.5 from Problem set 3. HOMEWORK 1, PROBLEMS 1.25, 1.30, 4.13 FROM PROBLEM SET 1 AND PROBLEMS 1.3, 2.21, 2.23 FROM PROBLEM SET 2. DUE DATE SEPTEMBER 16th

12. September the 2nd, 2020. Read section 3.3 from Reference 1. Support slides for the 11th class available here. Suggested problems: 1.3, 1.6, 1.7, 1.9, 1.14 from Problem set 3.

13. September the 3rd, 2020. Read section 3.4 from Reference 1, Support slides for the 12th class available here. Suggested problems 2.1, 2.2, 2.9, 2.10 from Problem set 3.

14. September the 8th, 2020. Problem set 4 available here. Read section 4.1 from Reference 1. Support slides for the 14th class available here. Suggested problems: 1, 3, 4, 5 from Problem set 4.

15. September the 9th, 2020. Read section 4.2 from Reference 1. Support slides for the 13th class available here. Suggested problems: 6, 7, 9, 10, 11, 12 from Problem set 4 .

16. September the 10th, 2020. Read section 4.3 from Reference 1, Support slides for the 14th class available here. Suggested problems 15, 16, 18 amd 20 from Problem set 4 .

17. September the 15th, 2020. Problem set 4 available here. Read section 4.4from Reference 1. Support slides for the 15th class available here. Suggested problems: 22, 23, 25, 27, 28 from Problem set 4.

18. September the 16th, 2020. FIRST VIRTUAL CLASS. Read sections 1.1 and 1.2 from Reference 1. Support slides for the first class available here. Debate Session, discussion of exercise 2.21 from Problem set 2.

19. September the 17th, 2020. Read section 1.2 and section 1.3 until the first paragraph of page 16. Support slides for the second class available here. Debate Session, discussion of problem 2.24 from Problem set 2.

20. September the 22nd, 2020. Read section 1.5, Support slides for the third class available here

21. September the 23rd, 2020. Read section 8.2 from Reference 1 and sections 6.3, 6.4 from Reference 2. Support slides for the fourth class available here.

22. September the 24th, 2020. Class suspended, due to SEMANA UNIVERSITARIA. We resume class on Tuesday September 29th. The graded papers of Homework 1 are available in the personalized shared folder of Google Drive

23. September the 29th, 2020. Read sections 2.1, 2. 2, 2.3 until the first paragraph of page 16. Support slides for the fifth class available here. The second half of the class was suspended due to CONNECTIVITY PROBLEMS. We resume class on September the 30th in the usual schedule.

24. September the 30th, 2020. Read section 2.4, 2.5, 2.6, Support slides for the sixth class available here.

25. October the 1st, 2020. Read section 4.3 from Reference 3. Support slides for the seventh class available here. TEST DATE OCTOBER 12th from 6:00 to 12:00.

26. October the 6th, 2020. Read sections 4.3, 4.4 from Reference 3. Support slides for the eighth class available here.

27. October the 7th, 2020. Read sections 4.5, 4.6 and 4.7 from Reference 3, Support slides for the ninth class available here.

28. October the 8th, 2020. Read sections 3.1, 3.2 from Reference 1. Support slides for the 10th class available here

29. October the 12th, 2020. Find HERE the firts test. You have until 12:00 M to submit your answers in this Google form

30. October the 13th, 2020. Read section 3.3 from Reference 1. Support slides for the 11th class available here.

31. October the 14th, 2020. Read section 3.4 from Reference 1, Support slides for the 12th class available here.

32. October the 15th, 2020. Read section 4.2 from Reference 1. Support slides for the 13th class available here. The class was suspended half way, because of internet connection problems. We will resume this class the next week.

33. October the 20th, 2020. Read section 4.2 from Reference 1. Support slides for the 13th class available here. HOMEWORK 2: 2.7, 2.20 and 3.5 from from Problem set 3, 14, 59 and 62 from from Problem set 4.

34. October the 21st, 2020. Read section 4.3 from Reference 1, Support slides for the 14th class available here, Read section 4.4from Reference 1. Support slides for the 15th class available here

35. October the 22nd, 2020. Read section 4.4 from Reference 1, Support slides for the 16th class available here . SECOND TEST, November the 8th, 6:00 to 12:00

36. October the 27th, 2020. Read section 6.5 from Reference 1, Support slides for the 17th class available here .

37. October the 28th, 2020. Read section 6.6 from Reference 1, Support slides for the 18th class available here . Problem set 5 Available here

38. October the 29th, 2020. Read section 5.1 and 5.2 from Reference 1, Support slides for the 19th class available here .

39. November the 3rd, 2020. Read section 5.3 from Reference 1, Support slides for the 20th class available here . Problem set 6 Available here

40. November the 8th, 2020. Find HERE the second test. You have until 12:00 M to submit your answers in this Google form

41. November the 9th, 2020. Homework 3, problems 17, 19, 26 from Problem set 5. Problems 1.27, 1.28 and 1.32 from Problem set 6, it is DUE Nombember the 30th at 6:00 AM. THIRD TEST SCHEDULED FOR NOVEMBER the 30th

42. November the 24th, 2020. The THIRD TEST will take place on November 29th from 6:00 AM to 12:00 M. The deadline for Homework 3 is November 29th at 6:00 AM. You can find it HERE.