Check up list the final: One-page cheat sheet is allowed
- Identify the premises and conclusions of an argument.
- Recognize fallacious arguments (you do not need to remember
particular names, but problems like 1A-15 might be asked)
- Truth tables of negation, disjuntion, conjuntion and
conditionals. Truth tables containing three propositions.
- Recognize conditionals, identify hypothesis and conclusion.
- Difference between or inclusive and or inclusive.
- Sets and relationship between sets (disjoint sets,
overlapping sets, sets included in other sets.)
- Four basic categorical propositions and their Venn diagram
representation. Negation of these propositions.
- Use of Venn diagrams for illustrating set relationships and
for organizing information.
- Recognize inductive and deductive arguments.
- How do you evaluate inductive arguments?
- How do you evaluate deductive arguments?
- Induction and deduction in mathematics.
- Units (Only material and problems from 2A): Idenify units.
Unit conversions. Currency conversions.
- Definition of outcomes and events.
- Count the total number of outcomes, and the number of
outcomes of an event. (The Multiplication Rule might be useful
here)
- IIdentify and compute theoretical and empirical
probability.
- Identfify independent, dependent, overlappping and
non-overlapping events. You should be able to apply correctly the
following formulae:
- If A and B are indepentent events then P(A and B) =
P(A) x P(B)
- If A and B are dependent, P(A and B) = P(A) x P(B
given A)
- P(A or B) = P(A) + P(B) - P(A and B). (Can this
formula be simplified if A and B are non-overlapping?)
- P(at least one occurrence of A in n trials)= 1 -
[P(A)]n (You should review the conditins under which this
formula can be
applied).
- Understand and apply the Law of Large Numbers.
- Compute expected value, and understand the results.
- Understand the Gamble's Fallacy.
- Compute an understand when to apply each of the following.
- Number selections of r objects from a set of n objects
are there? nr
- Permutations
- Combinations
- "At least once" rule.
- Compute probabilities using all the counting methods we saw.
- Understand meaning of population, sample, population parameters, sample statistics, placebo.
- Interpret histograms.
- Distribution, mean, median, mode, outlier,
- Atributes of a distribution: symmetrt skewness, unimodal, bimodal.
- Understand and compute and interpret: range, five-number summary, standar deviation.
- Describe normal distribution.
- Use a standard score table and apply the 68-95-99.7 rule.
- Understand and apply the concept of statistical significance. (at 0.05 level and 0.01 level), compute margin of error,.
- Undersdand hypothesis testing and interpret outcomes.
- Draw graphs to model problems.
- Underdstand circuit, Euler circuit, use the burning bridges rule to find Euler circuit.
- Understand spanning network, minimal spanning network and Kruskal's algorithm to find a minimal spanning network.
- Understand the traveling salesman problem, hamiltonian
circuits and the nearest neighbor method to find a Hamiltonian
circuit.
- Use a graph for the scheduling problem, find a critical path. The importance of the scheduling problems.
The final will have between 10 and 15 problems, similar to the
problems listed below.
Sample final (this does not mean that the statement of the problems
of the actual exam will be identical or extremely similar to that of
the ones listed below. It is just a guideline so you know the structure
and level of the exam.)
IMPORTANT: When
writing the answers to the final, make sure you explain how your
results were obtained. A numerical answer with no justification will
receive little or no credit.
- 1A-15;
- 1B-50;
1B-80; 1B-104
- 1C-76, 1C-82 1C-87, 1C-94;
- 1D-48; 1D-60;
- 2A 48 - 66 -86, 88
- 7A 52 -61 - 66 -
- 7B 24 -32- 42 46 - 58 - 62-66
- 7C 26- 34 - 44 -
- 7E 35- 38- 41- 45- 58 - 63- 65
- 6A - 39 - 49
- 6B- 28 - 30,
- 6C- 52 - 54 - 56
- 6D 28 - 36 - 52
- 13A 30 - 42 - 52
- 13B 31 - 32 -34
- 13C - 22 -34.-44 -46
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