Discrete Mathematics with Probability and Statistics
Recommended Prerequisite: Algebra I, Geometry, & Algebra II
Grades Offered: 9-12
Credit: 1/2-1
SDE Course Code: 3135
MNPS Course Code: MTH4515
Course Description:
Discrete Mathematics involves the study of objects and ideas that can be divided into separate or discontinuous parts. Problems to be studied can be classified into existence problems, counting problems, or optimization problems. This course will also acquaint the student with the theory of probability.
Outline of Content:
· The student will explore discrete mathematics.
° Applying discrete ideas to solve-real-world problems.
° Demonstrating an understanding of the elements, subsets, properties, operations of sets.
° Using valid forms of deductive reasoning and logic to make and evaluate arguments.
° Representing and solving problems using discrete structures such as finite graphs, matrices, and sequences.
° Using vertex-edge graphs to solve network problems such as finding circuits, critical paths, minimum spanning trees, and adjacency matrices.
° Analyzing and using discrete ideas such as induction, iteration, and recurrence relations to solve problems from such Chaos Theory, map Problems, and fractals.
° Creating tessellations using reflection, rotation, and translation.
· The student will explore probability.
° Applying number theory topics such as the Fundamental Theorem of Arithmetic, lowest common denominator, and greatest common factor, to solve problems using modular arithmetic.
° Creating and interpreting discrete probability distributions.
° Using experimental or theoretical probability to represent and solve problems involving uncertainty.
° Deriving and using formulas to calculate combinations and permutations.
° Understanding and applying the concept of random variables to generate and interpret probability distributions.
° Applying game theory to solve problems.
· The student will explore Statistics.
° Designing a statistical experiment to study a problem, conduct the experiment, and communicate and interpret the outcomes.
° Understanding and applying measures of central tendency, variability, and correlation to summarize data and draw inferences from real-world situations.
° Understanding sampling and recognizing its role in statistical claims.
° Conducting and interpreting test for significance using appropriate statistics.
° Using curve fitting to make predictions from data.
° Constructing and drawing inferences from charts, tables, and graphs that summarize data from real-world situations.
Standards Links:
MNPS Standards:
http://www.mnps.org/PageFactory.aspx?PageID=3403
State Standards:
http://www.state.tn.us/education/ci/cistandards2001/math/cimath.htm
Textbooks:
Basal: COMAP, For All Practical Purposes, 6th Edition, 2003, Bedford, Freeman, Worth (basal)
Online Textbook Activities:
http://bcs.whfreeman.com/fapp6/
Recommended/Required Resources:
- TI-83+ Graphing Calculator or TI-84+ Graphing Calculator
- Computer with internet access
- A variety of manipulatives: graph paper, rulers, protractors, two-color counters, fractionBars, centimeter cubes or linking cubes, geoboards, miras, Pattern blocks, algebra tiles, meter sticks, etc.
Website: www.colorado.edu/education/DMP
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