May 24, 2016
MGF 1107
Life Ratings Plummet in Venezuela, Thriving at 10-Year Low
Nearly half of residents of the country are struggling to afford food,
because of the low production it is not easy to
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4. September 5th: Naive set theory.
4.1. Sets: Basic denitions. Now that we are a little more experienced with
the basic language of logic, we can go back to our denition of set and review several
3. SEPTEMBER 3RD: MORE ABOUT LOGIC. TECHNIQUES OF PROOFS.
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3. September 3rd: More about logic. Techniques of proofs.
3.1. The behavior or quantiers under negation. Suppose a statement p
depends on a
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9. September 24th: Quotients modulo an equivalence relation.
9.1. Quotient of a set by an equivalence relation. Now that we know about
the link between equivalence relations and partitions, we can
5. SEPTEMBER 10TH: NAIVE SET THEORY: CARTESIAN PRODUCTS, RELATIONS.
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5. September 10th: Naive set theory: cartesian products, relations.
5.1. The cartesian product. Towards the end of 1.1, we mentio
6. SEPTEMBER 12TH: INDUCTION.
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6. September 12th: Induction.
6.1. The well-ordering principle and induction. We will come back to set
theory and relations very soon, but rst we take a moment to cove
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7. September 17th: Proof of the binomial theorem. Equivalence relations
and equivalence classes
7.1. The binomial theoremproof. Recall that at the end of the previous
section we stated the followin
10. SEPTEMBER 26TH: FUNCTIONS.
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10. September 26th: Functions.
10.1. Functions. Next we move to another fundamental type of relations: functions. You have used functions extensively in Calculus, and
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8. September 19th: Partitions and quotients.
8.1. Partitions and equivalence classes. A partition of a set A is a splitting
of A into a collection of disjoint subsets:
More precisely:
Definition 8.
12. OCTOBER 10TH: INJECTIVE, SURJECTIVE FUNCTIONS.
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12. October 10th: Injective, surjective functions.
12.1. Injections and surjections. You are probably familiar with the denitions that follow. The
MGF3301 practice questions
September 24, 2013
WARNING: These questions are not necessarily too similar to the questions that will be on
your test. Your test may be longer than this.
Express in correc
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11. October 8th: Functions: Composition, inverses.
11.1. Functions, recap. Here is a reminder of the situation: functions f : A !
B (that is, from a set A to a set B ) are (determined by) certain r
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13. October 15th: Isomorphisms
13.1. Isomorphisms of sets. As we observed above, Theorem 12.7 has the
following consequence: a function f : A ! B is an isomorphism (that is, it has a
two-sided inve
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16. October 24th: Dedekind cuts: existence of least upper bounds, and
decimal expansions
Before proving that D (unlike Q) is complete, we can verify that is a total order
in D, that is:
Proposition
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14. October 17th: Canonical decomposition
14.1. Canonical decomposition. Now that we have acquired some familiarity with injective and surjective functions, we can appreciate a simple but important
15. OCTOBER 22TH: DEDEKIND CUTS: DEFINITION AND EMBEDDING OF Q.
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15. October 22th: Dedekind cuts: denition and embedding of Q.
15.1. Real numbers: general considerations. Our next major task is a be
2. AUGUST 28TH: LOGIC
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2. August 28th: Logic
2.1. Logical connectives. Sets are specied by spelling out properties satised
by their elements. My examples have been a little sloppy, actually: when I w
1. AUGUST 26TH: BASIC NOTATION, QUANTIFIERS
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1. August 26th: Basic notation, quantiers
1.1. Sets: basic notation. In this class, Sets will simply be collections of
elements. Please realize that this
Quiz #11 (Form A) KEY
1) A proposed amendment to the U.S. Constitution has passed both the House and
the Senate with the required 2/3 super majority. Each state holds a vote on the
amendment and it re
Quiz #10 (Form B) KEY
ANSWERS ARE IN BOLD ITALICS.
1) Which number is next in the Fibonacci sequence of numbers: 1, 1, 2, 3, 5, 8, 13, 21 . .
a) 55
b) 1.62
c) 8
d) 34
2) Which of the following is NOT
Quiz #10 (Form A)
KEY
ANSWERS ARE IN BOLD ITALICS.
1) Which number is next in the Fibonacci sequence of numbers: 1, 1, 2, 3, 5, 8, 13, 21 . .
a) 55
b) 34
c) 8
d) 1.62
2) Which of the following is NOT
Quiz #9 (Form B)
KEY
March 31, 2004
Answers are in bold & italicized.
1) When an object can be shifted, say to the left or right, and still remain the same, it is
said to have:
a) reflection symmetry
Quiz #9 (Form A)
March 31, 2004
KEY
Answers are in bold & italicized.
1) The frequency of middle C is
a) 440 cps
b) 260 cps
c) 520 cps
d) 130 cps
2) The frequency of G one octave below middle G is:
a)
Quiz #8 (form A) KEY
Each problem is worth 1 point. You will not receive any partial credit for wrong answers on this quiz.
Everyone who takes the quiz begins with 4 points credit. Some answers have b
MGF 1107
Quiz #7 (form B)
KEY
Answers are in bold italics.
1) Consider a typical 30-year fixed-rate mortgage. During which of the following years is the highest portion of each
payment applied toward
MGF 1107
Quiz #7 (form A)
KEY
Answers are in bold italics.
1) Consider a typical 30-year fixed-rate mortgage. During which of the following years is the highest portion of each
payment applied toward
Quiz 6 Key
OCT. 15, 2004
1.) Dan deposits $300 each month into a retirement fund that pays 2.75% compounded monthly. How
much will he have in the account when he retires after working for 35 years?
PM
Quiz #6 (form A) KEY
Oct. 15, 2004
1.) Dan deposits $200 each month into a retirement fund that pays 3.75% compounded monthly. How
much will he have in the account when he retires after working for 35
Quiz #5 (Form B) KEY
Oct. 8, 2004
1.) You invest $6,250 in a saving account for a period of 3 years. How much money will you end up with
if your account pays 5.25% compounded . . .
a)
Quarterly? (2 po
Quiz #4 (Form B)
KEY Answers are in bold and italics.
1) Given the following set of test scores:
find the following:
a) Range
92
85
63
50
78
96
88
66
94 92
96 50 = 46
b) standard deviation
15.7
c) Est