Fundamental Concepts of Mathematics

LEC 02

MAT 511


Fall 2008
Mathematics department
Julia Viro

  • News: Exams results!

  • There are two sections of MAT 511, LEC 1 (Prof. Olga Plamenevskaya) and LEC 2 (Prof. Julia Viro). The sections will generally follow the same syllabus but not necessarily cover the same topics in the same weeks. The homework assignments will be different in the two sections. It is therefore crucial that you attend class in the section you are enrolled in.
    The webpage for MAT 511 LEC 1 is   http://www.math.sunysb.edu/~olga/mat511/index.html

  • Course description: This course aims to develop your appreciation of the logical basis of mathematics, and to lay the foundation for subsequent courses in the program. One of our goals will be to enhance your ability to understand and construct proofs. We will discuss fundamental ideas like number, set, and function; topics to be covered are
    1. Logic and proofs
    2. Mathematical induction
    3. Set theory, relations and partitions
    4. Functions
    5. Cardinality
    6. Axioms and construction for integers, rationals, and reals
    A more detailed schedule, along with homeworks, will be posted below as the course progresses.

  • Lectures: MW 5:20-6:40pm in Mathematics 4-130

  • Instructor: Julia Viro
    Office hours: M 10:45-11:45am in MLC and 11:45am-12:15pm in 3-119, F 10:45am-12:15pm in 3-119.

  • Textbook:  Smith,  Eggen, St. Andre,  A transition To Advanced Mathematics, Sixth Edition, Thomson Brooks/Cole

  • Homework is a compulsory part of the course. Under no circumstances will late homework be accepted.

    Homework Due date Assignment
    HW1 9/17 Ex. 1.1 nr. 5, 10 (g-m)
    Ex. 1.2 nr. 5 (f-k), 6 (d,e), 8 (f-k),  13 (f,g)
    Ex. 1.3 nr. 1 (k-m), 2 (k-m), 6 (a,c,e), 7 (b,c,e), 9 (a,b,d)
    HW2 9/22 Ex. 1.4 nr. 3 (d,e), 6 (a,b), 7(k),  8, 9 (c)
    Ex. 1.5 nr. 2, 7 (a)
    Ex. 1.6 nr. 1 (b,d), 4, 5 (b,c), 7 (b)
    Ex. 1.7 nr. 4 (a), 5 (c,d), 7(b)
    HW3 10/27 Ex. 2.1 nr. 3 (d,h,j), 4 (a-d), 5 (a,b),  6 (d), 11, 15
    Ex. 2.2 nr. 1 (b,d,f,h,j), 5, 10 (a,b,g), 14 (b)
    Ex. 2.3 nr. 1 (c,d,k), 6 (b), 11 (a,c)
    HW4 11/3 Ex. 2.4 nr. 1 (a-c), 7, 8 (b,d,g,j,l,s),  9 (b,e), 11
    Ex. 2.5 nr. 2, 4
    Ex. 2.6 nr. 5 , 6, 14, 17
    HW5 Ex. 4.1 nr. 3 (j), 9, 14,  16 (d)
    Ex. 4.2 nr. 1 (h), 14 (e)
    Ex. 4.3 nr. 6 , 9 (c,d), 14 (c)
    Ex. 4.4 nr. 6 (a,b,c,d)
    Ex. 5.2 nr. 1 (c), 2 (a,f), 3
    Ex. 3.1 nr. 6 (b,f)
    Ex. 3.2 nr. 1 (g,h,i), 4 (a,j), 8
    Ex. 3.3 nr. 3 (a,e), 4
    Ex. 3.4 nr. 8, 9

  • Recitations

    Recitation Date Problems for discussion
    R1 9/17 and 9/22 Ex. 1.4 nr. 3 (a,b), 6 (d), 8,  9 (a), 11 (a,b,c)
    Ex. 1.5 nr. 1 (a,b), 12
    Ex. 1.6 nr. 1 (a,c), 7 (i), 8
    Ex. 1.7 nr. 5 (a), 12
    R2 11/5 and 11/10 Ex. 2.2 nr. 15, 17
    Ex. 2.3 nr. 17, 18, 19
    Ex. 2.4 nr. 8 (e,f,h,i,m,o,q,r,u), 9 (a,d,f), 11
    Ex. 2.5 nr. 5, 15
    Ex. 2.6 nr. 2, 3, 10, 11, 18
    Ex. 3.1 nr. 3
    R3 12/1 Ex. 4.1 nr. 3 (a,e,f), 10, 16 (b)
    Ex. 4.2 nr. 1 (j), 6, 14 (g)
    Ex. 4.3 nr. 4 , 9 (a,b), 14 (a,b)
    Ex. 4.4 nr. 2 (a-f), 9, 14 (a,e), 18
    Ex. 5.2 nr. 1 (h), 2 (c,d)
    Ex. 3.1 nr. 6 (b,f)
    Ex. 3.2 nr. 1 (f,j), 4 (c,i), 15
    Ex. 3.3 nr. 3 (b,c), 7
    Ex. 3.4 nr. 7, 10

  • Exams: in-class tests and the final exam.

  • Tests

    Test Date Contents
    T1 9/24 Logic: propositions and connectives, truth tables, quantifiers, logical identities, construction of denials, deduction laws, proofs techniques.
    T2 11/12 Set theory: sets, subsets, Venn diagrams, operations on sets (intersection, union, difference, symmetric difference, complement), power set, Cartesian product of sets, indexed families of sets.
    Mathematical induction and its variants
    Combinatorics: principles of counting, inclusion-exclusion formulas, permutations, Pascal's triangle, binomial coefficients, binomial theorem.
    T3 12/3 Maps and related notions (domain, codomain, range, image, preimage, graph). Injective, surjective and bijective maps. Composition of maps, inverse map.
    Cardinality: finite and infinite sets, countable and uncountable sets, cardinal number.
    Relations. Reflexive, irreflexive, symmetric, weakly antisymmetric, transitive relations. Strict and nonstrict partial order. Equivalence relation, equivalence classes. Partition, quotient (factor) set, factorization map.

  • Make-up policy: Make-up examinations are given only for work missed due to unforeseen circumstances beyond the student's control.

  • Grading system: your grade for the course will be based on: homework 20%, in-class tests 60%, final exam 20%.

  • Disability support services (DSS) statement:
    If you have a physical, psychological, medical, or learning disability that may impact your course work, please contact Disability Support Services (631) 6326748 or http://studentaffairs.stonybrook.edu/dss/. They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential. Students who require assistance during emergency evacuation are encouraged to discuss their needs with their professors and Disability Support Services. For procedures and information go to the following website: http://www.stonybrook.edu/ehs/fire/disabilities/asp.

  • Academic integrity statement:
    Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another person's work as your own is always wrong. Faculty are required to report any suspected instance of academic dishonesty to the Academic Judiciary. For more comprehensive information on academic integrity, including categories of academic dishonesty, please refer to the academic judiciary website at http://www.stonybrook.edu/uaa/academicjudiciary/ .

  • Critical incident management:
    Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of Judicial Affairs any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, and/or inhibits students' ability to learn.