One service mathematics has rendered the human race. It has put common sense back where it belongs. It has put common sense back where it belongs, on the topmost shelf next to the dusty canister labelled discarded nonsense. (Eric T. Bell)
TuTh 3-4PM or by appointment in 423 Thackeray Hall.
Recitation instructor: Sahojar Khan
Between 1890 and 1930 mathematics underwent a modernist transformation in methodology, which shifted from the so-called scientific method, that relies on physical intuition and for which validity depends on comparison with external reality (explanations are valid as long as they are thoroughly tested), to the axiomatic method, that relies on precise definitions and on internal criteria for validity (rules and procedures that, when followed, produce completely reliable conclusions). The new methodology arose as a result of thousands of years of experimentation and allows modern mathematics to go considerably beyond what was previously accessible through the scientific method.
The course is an introduction to the modern methodology and forms the foundation on which all subsequent advanced courses in core mathematics will rest upon. The topics discussed will include logic, sets, functions, relations, numbers, and proofs. Classwork and homework will concentrate on assimilation of the modern methodology through the writing and understanding of proofs of theorems centered on these topics.
Math 0230.
A Transition to Advanced Mathematics. 8th edition by D. Smith, M. Eggen, R. St. Andre. The course covers (not necessarily in the same order) most of the material in Chapters 1-5 but also additional topics for which other resources will be indicated.
The following are also recommended
Introduction to Mathematical Thinking by K. Devlin, 2012.
Proofs from the Book by M. Aigner and G. Ziegler, 1999.
An Infinite Descent into Pure Mathematics. Version 0.6 by C. Newstead, May 29, 2024.
Mathematics: a Minimal Introduction by A. Buium, 2013.
The final grade will be computed from the following:
| Quizzes: | 5% | Daily |
| Homework: | 25% | Weekly |
| Exam 1: | 10% | Wednesday, February 4 |
| Exam 2: | 20% | Friday, March 6 |
| Exam 3: | 20% | Wednesday, April 8 |
| Exam 4: | 25% | Thursday, April 30, 12:00-1:50PM |
Due Thursday, January 22:
§1.1: 3(g,j), 4(d,h), 7(e-g), 10(e-f), 11(b, i-j).Due Thursday, January 29:
§1.2: 5, 6, 16(a-d), 12(a-b), 14.
§1.3: 1(a,e,g,h,m), 3, 5, 9(c,f,g), 10(e,j), 13.Due Thursday, February 5:
§1.4: 4(b,c,d), 5(d,e,g,j), 6(d,e,f), 11(b,e).Due Thursday, February 12:
§1.5: 4(d,e), 5(a,c), 6(e), 7(a,b), 9, 10, 11, 12(d,f).Due Thursday, February 19:
§1.6: 1(d,g), 2(d), 8(b,d), 9(c,f,h).
§2.1: 5, 10, 11(a,c,g), 15, 19(a,b,d,g,h,i).Due Thursday, February 26:
§2.2: 9(b,f), 10(e), 11(d), 15(c,d), 18, 20(e,f).
§2.4: 4(g,e), 5(a,e,j,m), 6(f), 12(a,c).Due Thursday, March 5:
§2.4: 5(q), 6(d,h), 7(a).Due Thursday, March 26:
§2.5: 1(a,c), 3, 14 (a,d,e,f).
§1.8: 6(a,b), 7, 9, 10.
§3.1: 1, 5, 10, 11.Due Thursday, April 2:
§3.2: 6(a,c,e,f), 7, 15, 17.
§3.3: 4(a,c,d,h), 15(a,b).
§4.1: 6(b,d), 14(a,b), 15(a,b), 18, 19(a,d).Due Thursday, April 9:
§4.2: 1, 4(b,c), 5.
§4.3: 5, 6, 9*, 11*, 13(a,c,d).
§4.4: 1, 3(a,c,d,e), 6*.
§4.5: 6(d-f), 7, 8, 10(b,d), 12 (e), 14(a,c).Due Thursday, April 16:
§5.1: 2(c,d), 3, 4, 10, 16, 18.
§5.2: 3(f-h), 4(a-c,e,h), 5, 7, 8, 12(b,c,h).
§5.3: 9, 10, 12, 16(a,c,d,f)