MAT 112.04

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This is a University Core Course in Mathematics taken by freshmen. Students in this course are expected to have successfully completed or placed out of MAT 110 and 111. The students in this course are introduced to topics on set theory and logic, probability, statistics, and applications. The students are trained in critical thinking and problem solving skills to be applied to real world situations. This course is the third of a three-sequence study in college general mathematics.

After completing this course successfully, the students would have acquired the following competencies:

Describe the meaning of the word "set" and write a given set in two different ways.

Identify well-defined sets and equal sets.

Find the subsets and proper subsets of a given set.

Identify the universal set and find the complement of a given set.

Find the union, intersection and difference of two sets or more.

Draw Venn diagrams to show the relationship between two or more sets.

Find the cardinal number of finite and infinite sets.

Use Venn diagrams to solve word problems.

Determine if a sentence is a "statement" and classify statements as simple or compound.

Identify a compound statement as a conjunction, disjunction, negation or conditional.

Write compound statements in symbolic form by using letters for each simple statement

and the proper logical connectives, and translate symbolic statements into verbal statements.

Construct a truth table for a given compound statement containing up to two variables.

Determine if two statements are logically equivalent by constructing truth tables.

Determine if an argument is valid or invalid by truth tables or Venn diagrams.

Find the probability of simple events

Find the probability of compound events

Find the conditional probability of events

Use counting principles to solve problems in probability

Use combinations and permutations to solve probability problems

Understand the uses and misuses of statistics and its terminology

Presentation of data in various forms - frequency distribution, bar diagrams, pie charts, frequency polygons

Compute mean, median, and mode for a raw data, frequency distribution

Compute standard deviation for a data

Use mean, standard deviation to analyze and interpret data.

Understand and use the normal distribution

compute linear correlation and fit regression lines for a given data

TOPIC OUTLINE:

Chapter 2: Sets: Set Concepts - Venn Diagrams and set operations - Venn Diagrams with three sets and verification of set statements - Application of sets - Infinite sets (Sections 2.1 to 2.6) (NCATE 5.12)

Chapter 3: Logic: Statements and logical connectives - Truth tables for negation, conjunction, and disjunction - Truth tables for the conditional and biconditional - Equivalent statements and DeMorgan’s Laws - The Conditional - Symbolic arguments (Sections 3.1 to 3.6) (NCATE 5.12, 5.15, 8.0, 8.1, 8.2, 8.3)

Chapter 12: Probability - Theoretical Probability - Odds - Expected Value - Tree diagrams - "or" and "and" problems - Conditional Probability - The Counting principle and permutations - Combinations - Solving Probability problems using permutations and combinations. (Sections 12.1 to 12.11) (NCATE 10.1)

Chapter 13: Statistics - Sampling techniques - The misuses of statistics - Frequency Distributions - Statistical Graphs - Measures of Central Tendency - Measures of Dispersion - The Normal Curve - Linear Correlation and Regression. (Sections 13.1 – 13.8) (NCATE 5.10, 5.11)

Quiz/Homework 30% of final grade

Tests 40% of final grade

Comprehensive final 30% of final grade

Students who miss classes are responsible for subject matter covered, any announcements made regarding quiz, test or any other relevant matter, during their absence.

More than 3 (if class meets 3 times a week) or 2 (if class meets 2 times a week) unexcused absences may result in failure in the course. You are responsible to find out or know about any announcements or the subject matter covered, during your absence.

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