1 |
Interpreting Categorical Data |
Interpreting
Categorical Data develops student understanding
of two-way frequency tables, conditional probability and
independence, and using data from a randomized experiment
to compare two treatments. |
Topics include two-way
tables, graphical representations, comparison of proportions
including absolute risk reduction and relative risk, characteristics
and terminology of well-designed experiments, expected frequency,
chi-square test of homogeneity, statistical significance. |
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2 |
Functions Modeling Change |
Functions
Modeling Change extends student understanding of
linear, exponential, quadratic, power, circular, and logarithmic
functions to model quantitative relationships and data
patterns whose graphs are transformations of basic patterns. |
Topics include linear,
exponential, quadratic, power, circular, and base-10 logarithmic
functions; mathematical modeling; translation, reflection,
stretching, and compressing of graphs with connections to
symbolic forms of corresponding function rules. |
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3 |
Counting Methods |
Counting Methods extends
student ability to count systematically and solve enumeration
problems using permutations and combinations. |
Topics include systematic
listing and counting, counting trees, the Multiplication
Principle of Counting, Addition Principle of Counting, combinations,
permutations, selections with repetition; the binomial theorem,
Pascal's triangle, combinatorial reasoning; and the general
multiplication rule for probability. |
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4 |
Mathematics of Financial Decision-Making |
Mathematics
of Financial Decision-Making extends student facility
with the use of linear, exponential, and logarithmic functions,
expressions, and equations in representing and reasoning
about quantitative relationships, especially those involving
financial mathematical models. |
Topics include forms
of investment, simple and compound interest, future value
of an increasing annuity, comparing investment options, continuous
compounding and natural logarithms; amortization of loans
and mortgages, present value of a decreasing annuity, and
comparing auto loan and lease options. |
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5 |
Binomial Distributions and Statistical
Inference |
Binomial Distributions
and Statistical Inference develops student understanding
of the rules of probability; binomial distributions; expected
value; testing a model; simulation; making inferences about
the population based on a random sample; margin of error;
and comparison of sample surveys, experiments, and observational
studies and how randomization relates to each. |
Topics include review
of basic rules and vocabulary of probability (addition and
multiplication rules, independent events, mutually exclusive
events); binomial probability formula; expected value; statistical
significance and P-value; design of sample surveys
including random sampling and stratified random sampling;
response bias; sample selection bias; sampling distribution;
variability in sampling and sampling error; margin of error;
and confidence interval. |
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6 |
Informatics |
Informatics develops
student understanding of the mathematical concepts and methods
related to information processing, particularly on the Internet,
focusing on the key issues of access, security, accuracy,
and efficiency. |
Topics include elementary
set theory and logic; modular arithmetic and number theory;
secret codes, symmetric-key and public-key cryptosystems;
error-detecting codes (including ZIP, UPC, and ISBN) and
error-correcting codes (including Hamming distance); and
trees and Huffman coding. |
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7 |
Spatial Visualization and Representations |
Spatial Visualization
and Representations extends student ability to visualize
and represent three-dimensional shapes using contour diagrams,
cross sections, and relief maps; to use coordinate methods
for representing and analyzing three-dimensional shapes
and their properties; and to use graphical and algebraic
reasoning to solve systems of linear equations and inequalities
in three variables and linear programming problems. |
Topics include using
contours to represent three-dimensional surfaces and developing
contour maps from data; sketching surfaces from sets of cross
sections; three-dimensional rectangular coordinate system;
sketching planes using traces, intercepts, and cross sections
derived from algebraic representations; systems of linear
equations and inequalities in three variables; and linear
programming. |
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8 |
Mathematics of Democratic Decision-Making |
Mathematics
of Democratic Decision-Making develops student understanding
of the mathematical concepts and methods useful in making
decisions in a democratic society, as related to voting
and fair division. |
Topics include preferential
voting and associated vote-analysis methods such as majority,
plurality, runoff, points-for-preferences (Borda method),
pairwise-comparison (Condorcet method), and Arrow's theorem;
weighted voting, including weight and power of a vote and
the Banzhaf power index; and fair division techniques, including
apportionment methods. |
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