### 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.
1. 1A-15;
2. 1B-50; 1B-80;  1B-104
3. 1C-76, 1C-82 1C-87, 1C-94;
4.  1D-48; 1D-60;
5. 2A 48 - 66 -86, 88
6. 7A 52 -61 - 66 -
7. 7B  24 -32- 42 46 - 58 - 62-66
8. 7C 26- 34 -  44 -
9. 7E  35- 38- 41- 45- 58 - 63- 65
10. 6A  - 39 - 49
11. 6B- 28 - 30,
12. 6C- 52 - 54 - 56
13. 6D 28 - 36 - 52
14. 13A 30 - 42 - 52
15. 13B 31 - 32 -34
16. 13C - 22 -34.-44 -46
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