Math 3345: Foundations of Higher Mathematics - AUTUMN 2015

Class Information

Time: 11:30AM-12:25PM
Days:: Monday, Wednesday, Friday
Place: 130 Baker Systems Engineering.
Textbook: The Fundamentals of Higher Mathematics, Autumn 2015 Edition, lecture notes by Professor Neil Falkner.
Material covered: Introduction to logic, proof techniques, set theory, number theory, real numbers.
Prerequisites: Major or minor in Math, CSE, CIS, or ECE, and: If Math: Prereq: A grade of C- or above in 2153, 2162.xx, 2173, or 2182H, or credit for 254.xx, 263.xx, 263.01H. If CIS, CSE or ECE: Prereq: A grade of C- or above in CSE 2321; and a grade of C- or above in 1161.xx, 1172, 1181H, 1534, 1544, 1152, or 4181H, or credit for 153.xx, 154, 162.xx, or 162.01H. Not open to students with credit for 345.
Syllabus: PDF version and HTMLversion.

Contact Information

Instructor: Davide Fusi
Office: MW 530
Office hours: Monday 12:40PM-1:40PM, Tuesday 1:45PM-2:45PM, Thursday 1:45PM-2:45PM, or by appointment
Phone: 614-292-5912
Email: fusi.1(AT)math(DOT)osu(DOT)edu or fusi.1(AT)osu(DOT)edu

Exams

Final: 17th of December (10:00am-11:45am in 130 Baker Systems Engineering).
Midterms: 28th of September and 9th of November.

Homework Assignments

Homework 1 (due on 9/4/2015): Exercises: 2, 4 (pag. 7).
Homework 2 (due on 9/9/2015): Exercises: 5 (pag. 8); 7 (pag. 9); 8 (pag. 11).
Homework 3 (due on 9/11/2015): Exercises: 10 (pag. 12); 13 (pag. 14); 21 (pag. 18).
Homework 4 (due on 9/14/2015): Exercises: 11 (pag. 12); 20 (pag. 18); 24 (pag. 20).
Homework 5 (due on 9/16/2015): Exercises: 1 parts: a, b, g, h (pag. 27); 5 (pag. 29).
Homework 6 (due on 9/18/2015): Exercises: 4 (pag. 29); 6 (pag. 30).
Homework 7 (due on 9/21/2015): Exercises: 10 parts: a, b (pag. 34); 11 (pag. 35); 14 parts: g, h. (pag. 36).
Homework 8 (due on 9/23/2015): Exercises: 14 parts: e, f (pag. 36); 2 (pag. 39); 5 (pag. 40).
Homework 9 (due on 9/25/2015): Exercises: 13 parts: b, c (pag. 44); 17 (pag. 47); 19 (pag. 47).
Homework 10 (due on 9/30/2015): Exercises: 20 (pag. 47); 26 part b (pag. 49); 2 (pag. 55).
Homework 11 (due on 10/2/2015): Exercises: 27 (pag. 50); 5 (pag. 56).
Homework 12 (due on 10/5/2015): Exercises: 1, 3 part: b, 4 (pag. 55).
Homework 13 (due on 10/7/2015): Exercises: 12, 13 part: a (pag. 61).
Homework 14 (due on 10/9/2015): Exercises: 2, 3 (pag. 69).
Homework 15 (due on 10/12/2015): Exercises: 4 (pag. 70).
Homework 16 (due on 10/14/2015): Exercises: 11 (pag. 43); 2 (pag. 80).
Homework 17 (due on 10/19/2015): Exercises: 1 (pag. 80); 4 (pag. 81).
Homework 18 (due on 10/21/2015): Exercises: 6 (pag. 82); 14 (pag. 61).
Homework 19 (due on 10/23/2015): Exercises: 14 (pag. 14); 26 (pag. 49); 11 (pag. 60).
Homework 20 (due on 10/26/2015): Exercises: 1 (pag. 100); 3 (pag. 101).
Homework 21 (due on 10/28/2015): Exercises: 4, 5 (pag. 102); 7 (pag. 103).
Homework 22 (due on 10/30/2015): Exercises: 9, 13 (pag. 104).
Homework 23 (due on 11/2/2015): Exercises: 15 (pag. 105); 21 (pag. 109).
Homework 24 (due on 11/4/2015): Exercises: 10 (pag. 104); 22, 23 (pag. 110).
Homework 25(due on 11/6/2015): Exercises: 33 part: b, c, d, e, f (pag. 114).
Homework 26(due on 11/13/2015): Exercises: 33 part: g, h (pag. 114); 1 (pag. 116).
Homework 27(due on 11/16/2015): Exercises: 4 part: a, b, c, d (pag. 119); 6, 10 (pag. 120).
Homework 28(due on 11/18/2015): Exercises: 27 (pag. 111); 5 part: a, b, c, d, e (pag. 119).
Homework 29(due on 11/20/2015): Exercises: 12, 13 (pag. 122).
Homework 30(due on 11/23/2015): Exercises: 17 (pag. 124), 22 (pag. 125).
Homework 31(due on 11/30/2015): Exercises: 1 (pag. 140), 3 (pag. 141), 23 (pag. 125).
Homework 32(due on 12/2/2015): Exercises: 5 (pag. 142), 6 (pag. 143), 19 (pag. 124).
Homework 33(due on 12/4/2015): Exercises: 7 (pag. 143), 8 (pag. 144).
Homework 34(due on 12/7/2015): Exercises: 1 (pag. 155), 3 (pag. 156), 5 (pag. 157).
Homework 35(due on 12/9/2015): Exercises: 6, 7 (pag. 157), 8 (pag. 158).

Course Calendar

Monday Wednesday Friday
August

26

Logical connectives: " ¬ ", " ∧ ", " ∨ ".

28

De Morgan’s laws; the distributive laws; conditional sentences: " ⇒ ".

31

Logical connectives: " ⇐ ", " ⇔ "; conditional proof.

September

2

Modus ponens; proof by contradiction.

4

Proof by contraposition; quantifiers: " ∀ ", " ∃ "; common sets of numbers.

7

LABOR DAY

9

Examples and counterexamples; free and bound variables; generalized De Morgan`s laws.

11

Generalized distributive laws.

14

Order of quantifiers; uniqueness; even numbers and odd numbers.

16

Rational numbers; irrational numbers.

18

Divisibility; prime numbers.

21

Congruences of integers; induction.

23

Review

25

More induction.

28

MIDTERM 1

30

Pascal's triangle.

October

2

Sums of powers revisited.

5

Sums of geometric progressions.

7

Complete induction.

9

More complete induction.

12

More complete induction.

14

More complete induction; review of proofs.

16

Autumn Break

19

Sets: definition, description and examples.

21

Sets: empty set, union, intersection.

23

Sets: relative complement, Venn Diagrams.

26

Sets: disjointness, intervals

28

Unions and intersections of sets of sets

30

The power set of a set; cartesian product.

November

2

Functions: definition and examples

4

Review

6

Functions: composition and range

9

MIDTERM 2

11

Veterans Day

13

Restriction and extension of functions; surjective and injective functions.

16

Functions: bijections and examples.

18

Functions: properties of bijections.

20

Equinumerosity

23

The fundamental property of finite sets.

25

Thanksgiving Break

27

Columbus Day

30

The fundamental property of infinite sets; Infinite sets equinumerous to ℕ

December

2

Examples of bijections between intervals (and real line)

4

Cantor's Theorems

7

Some useful exercises

9

Review

Other Announcements

  • Office hours end of the semester:
    Friday December 11: 3:30pm-5:00pm;
    Monday December 14: 10:00am-11:30am; and
    Wednesday December 16: 3:30pm-5:00pm.

  • Midterm 1 Practice Exam: PDF file

    Students with Disabilities

    Students with disabilities that have been certified by the Office for Disability Services will be appropriately accommodated, and should inform the instructor as soon as possible of their needs.

    The Office for Disability Services is located in 150 Pomerene Hall, 1760 Neil Avenue; telephone (614) 292-3307 and VRS (614) 429-1334.