Discrete Mathematics with Statistics and Probability
Course description:
Discrete Mathematics with Statistics and Probability is an
advanced course that includes using discrete structures to represent and determine
solutions to problem situations; collecting, representing, and processing data;
and applying probability in problem-solving.
Standard 1.0: Discrete Mathematics
Students will investigate meaningful problems individually
or in cooperative groups, while using appropriate technology, to apply discrete
structures to represent and solve problems.
Learning Expectations:
The student will:
- 1.1 use discrete
structures to represent problem situations;
- 1.2 apply inductive
and deductive reasoning to discrete problem situations;
- 1.3 apply discrete
ideas and structures to solve a variety of problems.
Student Performance Indicators:
- apply
discrete ideas to solve real-world problems (i.e. election theory, group ranking,
and estate planning);
- demonstrate
an understanding of the elements, subsets, properties, operations of sets;
- use
valid forms of deductive reasoning and logic to make and evaluate arguments;
- represent
and solve problems using discrete structures such as finite graphs, matrices,
and sequences (e.g. Leslie Model, Leontief Model, Markov Chain, and cryptographic
techniques);
- use
vertex-edge graphs to solve network problems such as finding circuits,
critical paths, minimum spanning trees, and adjacency matrices;
- analyze
and use discrete ideas such as induction, iteration, and recurrence relations
to solve problems from such fields as Chaos Theory, Map Problems, and fractals;
- create
tessellations using reflection, rotation, and translation.
Standard 2.0: Probability
- 2.1 demonstrate
an understanding of probability distributions;
- 2.2 apply experimental
and theoretical probability in problem solving;
- apply
number theory topics such as the Fundamental Theorem of Arithmetic, lowest
common denominator, greatest common factor, etc. to solve problems using modular
arithmetic;
- create
and interpret discrete probability distributions;
- use
experimental or theoretical probability, as appropriate, to represent and
solve problems involving uncertainty;
- derive
and use formulas to calculate combinations and permutations;
- understand
and apply the concept of a random variable to generate and interpret probability
distributions including binomial, uniform, normal, and Chi Square; apply
game theory to problem solving.
Standard 3.0: Statistics
Students will select and use appropriate representations and
statistical methods to analyze data collected from real-world situations.
Learning Expectations:
- 3.1 formulate
questions and design appropriate studies;
- 3.2 select and
use appropriate representations to summarize data;
- 3.3 select and
use appropriate statistics to analyze data.
- design
a statistical experiment to study a problem, conduct the experiment, and communicate
and interpret the outcomes;
- understand
and apply measures of central tendency, variability, and correlation to
summarize data and draw inferences from real-world situations;
- understand
sampling and recognize its role in statistical claims;
- conduct
and interpret tests for significance using appropriate statistics;
- use
curve fitting to make predictions from data;
- construct
and draw inferences from charts, tables, and graphs that summarize data
from real-world situations.
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