- \r\n \t
- Define and use the elements of a graph to optimize paths through the graph<\/li>\r\n \t
- Identify the number of vertices and edges on a graph<\/li>\r\n \t
- Determine whether a graph is connected<\/li>\r\n \t
- Define the degree of a vertex of a graph<\/li>\r\n \t
- Determine the difference between a path and a circuit<\/li>\r\n \t
- Use Dijkstra\u2019s algorithm to find the shortest path between two vertices<\/li>\r\n \t
- Given a table of driving times between cities, find the shortest path between two cities<\/li>\r\n \t
- Define an Euler path, and an Euler circuit<\/li>\r\n \t
- Use Fleury\u2019s algorithm to determine whether a graph has an Euler circuit<\/li>\r\n<\/ul>\r\n
Module 5: Fractals<\/h2>\r\n
- \r\n \t
- Generate a fractal with random variation<\/li>\r\n \t
- Calculate Fractal Dimension using scaling relation<\/li>\r\n \t
- Identify and make arithmetic calculations with imaginary numbers<\/li>\r\n \t
- Plot complex numbers on the complex plane<\/li>\r\n \t
- Define a recursive sequence that will generate a fractal in the complex plane<\/li>\r\n \t
- Determine\u00a0whether a complex number is part of the Mandlebrot set<\/li>\r\n<\/ul>\r\n
Module 6: Theory and Logic<\/h2>\r\n
- \r\n \t
- Describe memberships of sets, including the empty set, using proper notation, and decide whether given items are members and determine the cardinality of a given set<\/li>\r\n \t
- Perform the operations of union, intersection, complement, and difference on sets using proper notation<\/li>\r\n \t
- Describe the relations between sets regarding membership, equality, subset, and proper subset, using proper notation<\/li>\r\n \t
- Be able to draw and interpret Venn diagrams of set relations and operations and use Venn diagrams to solve problems<\/li>\r\n \t
- Recognize when set theory is applicable to real-life situations, solve real-life problems, and communicate real-life problems and solutions to others<\/li>\r\n \t
- Combine sets using Boolean logic, using proper notations<\/li>\r\n \t
- Use statements and conditionals to write and interpret expressions<\/li>\r\n \t
- Use a truth table to interpret complex statements or conditionals<\/li>\r\n \t
- Write truth tables given a logical implication, and it\u2019s related\u00a0statements \u2013 converse, inverse, and contrapositive<\/li>\r\n \t
- Determine whether two statements are logically equivalent<\/li>\r\n \t
- Use DeMorgan\u2019s laws to define logical equivalences of a statement<\/li>\r\n \t
- Discern between an inductive argument and a deductive argument<\/li>\r\n \t
- Evaluate deductive arguments<\/li>\r\n \t
- Analyze arguments with Venn diagrams and truth tables<\/li>\r\n \t
- Use logical inference to infer whether a statement is true<\/li>\r\n \t
- Identify logical fallacies in common language including appeal to ignorance, appeal to authority, appeal to consequence, false dilemma, circular reasoning, post hoc, correlation implies causation, and straw man arguments<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n
\r\n Module 7: Voting Theory<\/h2>\r\n
- \r\n \t
- Given the results of a preference ballot, determine the winner of an election using the plurality method<\/li>\r\n \t
- Identify flaws in the plurality voting method<\/li>\r\n \t
- Identify situations that may lead to insincere voting<\/li>\r\n \t
- Given the results of a preference ballot, determine the winner of an election\u00a0using the instant runoff voting method<\/li>\r\n \t
- Identify situations when the instant runoff voting method produces a violation of the Condorcet Winner<\/li>\r\n \t
- Given the results of a preference ballot, determine the winner of an election using the Borda Count<\/li>\r\n \t
- Identify situations where the Borda count violates the fairness criterion<\/li>\r\n \t
- Given the results of a preference ballot, determine the winner of an election using Copeland\u2019s method<\/li>\r\n \t
- Identify situations where Copeland\u2019s method violates the independence of irrelevant alternatives criterion<\/li>\r\n \t
- Given the results of an approval ballot determine the winner of an election<\/li>\r\n \t
- Identify how approval voting can violate the majority criterion<\/li>\r\n<\/ul>\r\n
Module 8: Growth Models<\/h2>\r\n
- \r\n \t
- Build a recursive equation that models linear or exponential growth<\/li>\r\n \t
- Build an explicit equation that models linear or exponential growth<\/li>\r\n \t
- Make predictions using linear and exponential growth models<\/li>\r\n \t
- Use logarithms to solve exponential growth models for time<\/li>\r\n \t
- Identify the carrying capacity and growth rate of the logistic growth model<\/li>\r\n \t
- Use the logistic growth model to make predictions<\/li>\r\n<\/ul>\r\n
Module 9: Finance<\/h2>\r\n
- \r\n \t
- Calculate future value and payments for savings annuities problems<\/span><\/li>\r\n \t
- Calculate present value and payments for payout annuities problems<\/span><\/li>\r\n \t
- Calculate present value and payments for loans problems<\/span><\/li>\r\n \t
- Determine the appropriate financial formula to use given a scenario by recognizing key words and examining frequency of deposits or withdrawals, and whether account is growing or decreasing in value<\/span><\/li>\r\n \t
- Analyze a home mortgage refinance scenario, forming judgments by combining calculations and opinion<\/span><\/li>\r\n \t
- Solve a financial application for time using logarithms<\/span><\/li>\r\n<\/ul>\r\n
Module 10: Statistics: Collecting Data<\/h2>\r\n
- \r\n \t
- Define the population and the parameters of a study<\/li>\r\n \t
- Discern between a census and a population<\/li>\r\n \t
- Define the sample and statistics of a study<\/li>\r\n \t
- Classify data as categorical or quantitative<\/li>\r\n \t
- Identify an appropriate sample for a study<\/li>\r\n \t
- Identify possible sources of sampling bias<\/li>\r\n \t
- Identify different techniques for sampling data<\/li>\r\n<\/ul>\r\n
Module 11: Statistics: Describing Data<\/h2>\r\n
- \r\n \t
- Present categorical data graphically using a frequency table, bar graph, Pareto chart, pie charts, pictograms<\/li>\r\n \t
- Present quantitative data graphically using histograms, frequency tables,\u00a0pie charts, or frequency polygons<\/li>\r\n \t
- Define the measures of central tendency for a sample of data including mean, median, mode<\/li>\r\n \t
- Define measures of variation of a sample of data including range, standard deviation, quartiles, box plots<\/li>\r\n<\/ul>\r\n
Module 12: Probability<\/h2>\r\n
- \r\n \t
- Describe a sample space and simple and compound events in it using standard notation<\/li>\r\n \t
- Calculate the probability of an event using standard notation<\/li>\r\n \t
- Calculate the probability of two independent events using standard notation<\/li>\r\n \t
- Recognize when two events are mutually exclusive<\/li>\r\n \t
- Calculate a conditional probability using standard notation<\/li>\r\n \t
- Compute a conditional probability for an event<\/li>\r\n \t
- Use Baye\u2019s theorem to compute a conditional probability<\/li>\r\n \t
- Calculate the expected value of an event<\/li>\r\n<\/ul>\r\n<\/section>","rendered":"
![\"icon](\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2018\/01\/11222955\/outcomes.jpg\")
<\/p>\nThe textbook\u00a0content, assignments, and assessments for Mathematics for Liberal Arts are aligned to the following learning outcomes:<\/p>\n
Module 1: Historical Counting Systems<\/h2>\n
- \n
- Explore the counting and number system used by the Inca<\/li>\n
- Become familiar with the evolution of our current counting method<\/li>\n
- Convert between Hindu-Arabic and Roman Numerals<\/li>\n
- Become familiar with the history of positional number systems<\/li>\n
- Identify bases that have been used in number systems historically<\/li>\n
- Convert numbers between bases other than 10<\/li>\n
- Use two different methods for converting numbers between bases<\/li>\n<\/ul>\n
Module 2: General Problem Solving<\/h2>\n
- \n
- Write an equivalent fraction or decimal given a percent<\/li>\n
- Find a percent of a whole<\/li>\n
- Calculate absolute and relative change given two quantities<\/li>\n
- Express a relationship as a rate<\/li>\n
- Write a proportion equation given two rates or ratios, solve the proportion equation<\/li>\n
- Determine when two quantities don\u2019t scale proportionally, or more information is needed to determine whether they do<\/li>\n
- Solve problems using basic geometry to calculate area<\/li>\n
- Solve problems using basic geometry to calculate volume<\/li>\n
- Proportions, similar triangles, ratios applied to geometric problems<\/li>\n
- Define and implement a \u201csolution pathway\u201d for solving mathematical problems<\/li>\n
- Calculate sales tax, property tax<\/li>\n
- Calculate flat tax, progressive tax, and regressive tax<\/li>\n
- <\/li>\n<\/ul>\n
Module 3: Measurement<\/h2>\n
- \n
- Define units of length, weight, and capacity and convert from one to another.<\/li>\n
- Perform arithmetic calculations on units of length, weight, and capacity.<\/li>\n
- Solve application problems involving units of length, weight, and capacity.<\/li>\n
- Describe the general relationship between the U.S. customary units and metric units of length, weight\/mass, and volume.<\/li>\n
- Define the metric prefixes and use them to perform basic conversions among metric units.<\/li>\n
- Solve application problems involving metric units of length, mass, and volume.<\/li>\n
- State the freezing and boiling points of water on the Celsius and Fahrenheit temperature scales.<\/li>\n
- Convert from one temperature scale to the other, using conversion formulas.<\/li>\n<\/ul>\n
Module 4: Graph Theory<\/h2>\n
\n\n- \n
- Define and use the elements of a graph to optimize paths through the graph<\/li>\n
- Identify the number of vertices and edges on a graph<\/li>\n
- Determine whether a graph is connected<\/li>\n
- Define the degree of a vertex of a graph<\/li>\n
- Determine the difference between a path and a circuit<\/li>\n
- Use Dijkstra\u2019s algorithm to find the shortest path between two vertices<\/li>\n
- Given a table of driving times between cities, find the shortest path between two cities<\/li>\n
- Define an Euler path, and an Euler circuit<\/li>\n
- Use Fleury\u2019s algorithm to determine whether a graph has an Euler circuit<\/li>\n<\/ul>\n
Module 5: Fractals<\/h2>\n
- \n
- Generate a fractal with random variation<\/li>\n
- Calculate Fractal Dimension using scaling relation<\/li>\n
- Identify and make arithmetic calculations with imaginary numbers<\/li>\n
- Plot complex numbers on the complex plane<\/li>\n
- Define a recursive sequence that will generate a fractal in the complex plane<\/li>\n
- Determine\u00a0whether a complex number is part of the Mandlebrot set<\/li>\n<\/ul>\n
Module 6: Theory and Logic<\/h2>\n
- \n
- Describe memberships of sets, including the empty set, using proper notation, and decide whether given items are members and determine the cardinality of a given set<\/li>\n
- Perform the operations of union, intersection, complement, and difference on sets using proper notation<\/li>\n
- Describe the relations between sets regarding membership, equality, subset, and proper subset, using proper notation<\/li>\n
- Be able to draw and interpret Venn diagrams of set relations and operations and use Venn diagrams to solve problems<\/li>\n
- Recognize when set theory is applicable to real-life situations, solve real-life problems, and communicate real-life problems and solutions to others<\/li>\n
- Combine sets using Boolean logic, using proper notations<\/li>\n
- Use statements and conditionals to write and interpret expressions<\/li>\n
- Use a truth table to interpret complex statements or conditionals<\/li>\n
- Write truth tables given a logical implication, and it\u2019s related\u00a0statements \u2013 converse, inverse, and contrapositive<\/li>\n
- Determine whether two statements are logically equivalent<\/li>\n
- Use DeMorgan\u2019s laws to define logical equivalences of a statement<\/li>\n
- Discern between an inductive argument and a deductive argument<\/li>\n
- Evaluate deductive arguments<\/li>\n
- Analyze arguments with Venn diagrams and truth tables<\/li>\n
- Use logical inference to infer whether a statement is true<\/li>\n
- Identify logical fallacies in common language including appeal to ignorance, appeal to authority, appeal to consequence, false dilemma, circular reasoning, post hoc, correlation implies causation, and straw man arguments<\/li>\n<\/ul>\n<\/div>\n<\/div>\n
\n Module 7: Voting Theory<\/h2>\n
- \n
- Given the results of a preference ballot, determine the winner of an election using the plurality method<\/li>\n
- Identify flaws in the plurality voting method<\/li>\n
- Identify situations that may lead to insincere voting<\/li>\n
- Given the results of a preference ballot, determine the winner of an election\u00a0using the instant runoff voting method<\/li>\n
- Identify situations when the instant runoff voting method produces a violation of the Condorcet Winner<\/li>\n
- Given the results of a preference ballot, determine the winner of an election using the Borda Count<\/li>\n
- Identify situations where the Borda count violates the fairness criterion<\/li>\n
- Given the results of a preference ballot, determine the winner of an election using Copeland\u2019s method<\/li>\n
- Identify situations where Copeland\u2019s method violates the independence of irrelevant alternatives criterion<\/li>\n
- Given the results of an approval ballot determine the winner of an election<\/li>\n
- Identify how approval voting can violate the majority criterion<\/li>\n<\/ul>\n
Module 8: Growth Models<\/h2>\n
- \n
- Build a recursive equation that models linear or exponential growth<\/li>\n
- Build an explicit equation that models linear or exponential growth<\/li>\n
- Make predictions using linear and exponential growth models<\/li>\n
- Use logarithms to solve exponential growth models for time<\/li>\n
- Identify the carrying capacity and growth rate of the logistic growth model<\/li>\n
- Use the logistic growth model to make predictions<\/li>\n<\/ul>\n
Module 9: Finance<\/h2>\n
- \n
- Calculate future value and payments for savings annuities problems<\/span><\/li>\n
- Calculate present value and payments for payout annuities problems<\/span><\/li>\n
- Calculate present value and payments for loans problems<\/span><\/li>\n
- Determine the appropriate financial formula to use given a scenario by recognizing key words and examining frequency of deposits or withdrawals, and whether account is growing or decreasing in value<\/span><\/li>\n
- Analyze a home mortgage refinance scenario, forming judgments by combining calculations and opinion<\/span><\/li>\n
- Solve a financial application for time using logarithms<\/span><\/li>\n<\/ul>\n
Module 10: Statistics: Collecting Data<\/h2>\n
- \n
- Define the population and the parameters of a study<\/li>\n
- Discern between a census and a population<\/li>\n
- Define the sample and statistics of a study<\/li>\n
- Classify data as categorical or quantitative<\/li>\n
- Identify an appropriate sample for a study<\/li>\n
- Identify possible sources of sampling bias<\/li>\n
- Identify different techniques for sampling data<\/li>\n<\/ul>\n
Module 11: Statistics: Describing Data<\/h2>\n
- \n
- Present categorical data graphically using a frequency table, bar graph, Pareto chart, pie charts, pictograms<\/li>\n
- Present quantitative data graphically using histograms, frequency tables,\u00a0pie charts, or frequency polygons<\/li>\n
- Define the measures of central tendency for a sample of data including mean, median, mode<\/li>\n
- Define measures of variation of a sample of data including range, standard deviation, quartiles, box plots<\/li>\n<\/ul>\n
Module 12: Probability<\/h2>\n
- \n
- Describe a sample space and simple and compound events in it using standard notation<\/li>\n
- Calculate the probability of an event using standard notation<\/li>\n
- Calculate the probability of two independent events using standard notation<\/li>\n
- Recognize when two events are mutually exclusive<\/li>\n
- Calculate a conditional probability using standard notation<\/li>\n
- Compute a conditional probability for an event<\/li>\n
- Use Baye\u2019s theorem to compute a conditional probability<\/li>\n
- Calculate the expected value of an event<\/li>\n<\/ul>\n<\/section>\n\n\t\t\t
\n\t\t\t Candela Citations<\/h3>\n\t\t\t\t\t
\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tCC licensed content, Original<\/div>- Course Learning Outcomes. Provided by<\/strong>: Lumen Learning. License<\/strong>: CC BY: Attribution<\/a><\/em><\/li><\/ul>CC licensed content, Shared previously<\/div>
- Magnify. Authored by<\/strong>: Eucalyp. Provided by<\/strong>: Noun Project. Located at<\/strong>: https:\/\/thenounproject.com\/term\/magnify\/1276779\/<\/a>. License<\/strong>: CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":31,"menu_order":1,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Magnify\",\"author\":\"Eucalyp\",\"organization\":\"Noun Project\",\"url\":\"https:\/\/thenounproject.com\/term\/magnify\/1276779\/\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Course Learning Outcomes\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"front-matter-type":[],"contributor":[],"license":[],"class_list":["post-2798","front-matter","type-front-matter","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/pressbooks\/v2\/front-matter\/2798","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/pressbooks\/v2\/front-matter"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/wp\/v2\/types\/front-matter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/wp\/v2\/users\/31"}],"version-history":[{"count":2,"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/pressbooks\/v2\/front-matter\/2798\/revisions"}],"predecessor-version":[{"id":2865,"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/pressbooks\/v2\/front-matter\/2798\/revisions\/2865"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/pressbooks\/v2\/front-matter\/2798\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/wp\/v2\/media?parent=2798"}],"wp:term":[{"taxonomy":"front-matter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/pressbooks\/v2\/front-matter-type?post=2798"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/wp\/v2\/contributor?post=2798"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/wp\/v2\/license?post=2798"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
- Course Learning Outcomes. Provided by<\/strong>: Lumen Learning. License<\/strong>: CC BY: Attribution<\/a><\/em><\/li><\/ul>
- Calculate present value and payments for payout annuities problems<\/span><\/li>\n
- Calculate future value and payments for savings annuities problems<\/span><\/li>\n
- Calculate present value and payments for payout annuities problems<\/span><\/li>\r\n \t
- Calculate future value and payments for savings annuities problems<\/span><\/li>\r\n \t