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Discrete Math

 

 

 Note: Homework assignments are always on the last slide of the lecture

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Date Objectives
  Lectures
  Section 1 - Number Bases    
1/5 Orientation

   
1/6-1/7

Students will understand numbers, ways of representing numbers, relationships among numbers and number systems.  The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment.
 CFU:3135.2.1 Use calculators appropriately and make estimations without a calculator regularly to detect potential errors.

  

  1.1-Converting Bases

1.1-Practice Problems
1/10-1/11

Students will understand numbers, ways of representing numbers, relationships among numbers and number systems.  Students will also learn to convert numbers between bases 2, 8, 10, and 16. The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment.
 CFU:3135.2.5 Compare ancient numeral systems in various bases to base t and base 8 numerals.

 

  1.2-Converting Bases

1.2a-Practice Problems

1.2b-Practice Problems
1/12-1/13

Students will understand numbers, ways of representing numbers, relationships among numbers and number systems.  Students will also learn to convert numbers between bases 2, 8, 10, and 16. The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment.
 CFU:3135.2.5 Compare ancient numeral systems in various bases to base t and base 8 numerals.

 

  1.3-Adding Bases


 1/14-1/18

Students will learn to perform basic arithmetic operations between base 2, 8, 10 and 16 numbers.  The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment.
 CFU:3135.2.6 Perform familiar arithmetic processes in base 2, base 8 and base 12.

  

  1.4-Subtracting Bases

1.4-Practice Prolems
1/21 Students willl learn to convert numbers of base 2, 8, 10 and 16 to all other bases using a spreadhseet.
 CFU:3135.2.1 Use calculators appropriately and make estimations without a calculator regularly to detect potential errors.
 3135.2.7 Develop individual examples that demonstrate different types of numerical computer errors. Also, demonstrate how computers can take introductory minimal errors and magnify them to errors of much larger order of magnitude.
 
   
1/24 Review
 
   
1/25 Section 1 Exam
 
   
       
  Section 2 - Series, Sequence, Iteration/Recursion & Binomial Theorem    
1/26-1/27

Students will be able to define An Arithmetic Sequence and Arithmetic Mean. Students will be able to accurately predict the nth term of a sequence by developing a model based on given information.  The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment.
 CFU:3135.1.6 Apply various problem-solving strategies to model and interpret physical, social, and mathematical phenomena.

  

  2.1-Arithmetic Sequence
 

Students will be able to define An Arithmetic Sequence and Arithmetic Mean. Students will be able to accurately predict the nth term of a sequence by developing a model based on given information.  The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment.
 CFU:3135.1.6 Apply various problem-solving strategies to model and interpret physical, social, and mathematical phenomena.
 

  2.1a-Practice Problems
 1/28-1/31

Students will be able to define An Arithmetic Series. Students will be able to accurately predict the nth term of a series by developing a model based on given information.  The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment.
 CFU:3135.1.6 Apply various problem-solving strategies to model and interpret physical, social, and mathematical phenomena.

 

  2.2-Arithmetic Series
 

Students will be able to define An Arithmetic Series. Students will be able to accurately predict the nth term of a series by developing a model based on given information.  The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment.
 CFU:3135.1.6 Apply various problem-solving strategies to model and interpret physical, social, and mathematical phenomena.

 

  2.2a-Practice Problems
2/1-2/2

Students will be able to define A Geometric Sequence. Students will be able to accurately predict the nth term of a sequence by developing a model based on given information.  The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment.
 CFU:3135.1.6 Apply various problem-solving strategies to model and interpret physical, social, and mathematical phenomena.

  

  2.3-Geometric Sequence
 

Students will be able to define A Geometric Sequence. Students will be able to accurately predict the nth term of a sequence by developing a model based on given information.  The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment.
 CFU:3135.1.6 Apply various problem-solving strategies to model and interpret physical, social, and mathematical phenomena.
 

  2.3-Practice Problems

2.3a-Practice Problems
 2/3-2/4  Students will be able to define A Geometric Series. Students will be able to accurately predict the nth term of a series by developing a model based on given information.  The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment. 
 CFU:3135.1.6 Apply various problem-solving strategies to model and interpret physical, social, and mathematical phenomena.

 
  2.4-Geometric Series
  Students will be able to define A Geometric Series. Students will be able to accurately predict the nth term of a series by developing a model based on given information.  The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment. 
 CFU:3135.1.6 Apply various problem-solving strategies to model and interpret physical, social, and mathematical phenomena.
 
  2.4a-Practice Problems
2/7-2/8  Students will be able to define An Infinite Geometric Series. Students will be able to accurately predict the nth term of a series by developing a model based on given information.  Students will also be able to solve equations using Recursion. Students will be able to defind a Fibonacci Sequence, predict it to the nth term and understand where they occur in nature. The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment.
 CFU:3135.1.6 Apply various problem-solving strategies to model and interpret physical, social, and mathematical phenomena.
 
  2.5-Infinite Geometric Series, Recursion and Special Sequences
   Students will be able to define An Infinite Geometric Series. Students will be able to accurately predict the nth term of a series by developing a model based on given information.  Students will also be able to solve equations using Recursion. Students will be able to defind a Fibonacci Sequence, predict it to the nth term and understand where they occur in nature. The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment.
 CFU:3135.1.6 Apply various problem-solving strategies to model and interpret physical, social, and mathematical phenomena.

 
  2.5a-Practice Problems
2/9-2/11 Students will be able to construct a Pascal's Triangle and use it to determine the nth term of an expanded binomial expression taken to the nth term. The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment. 
 CFU:3135.1.6 Apply various problem-solving strategies to model and interpret physical, social, and mathematical phenomena.
 
  2.6-Binomial Theorem
  Students will be able to construct a Pascal's Triangle and use it to determine the nth term of an expanded binomial expression taken to the nth term. The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment. 
 CFU:3135.1.6 Apply various problem-solving strategies to model and interpret physical, social, and mathematical phenomena
.
 
  2.6a-Practice Problems
  Students will be able to construct a Pascal's Triangle and use it to determine the nth term of an expanded binomial expression taken to the nth term. The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment. 
 CFU:3135.1.6 Apply various problem-solving strategies to model and interpret physical, social, and mathematical phenomena.

 
  2.6b-Practice Problems
2/14 Students will learn to write an Excel Spreadsheet to perform iteration in order to achieve a reasonable answer within prescribed limitations. Students will also use Excel to calculate payoff amounts on interest bearing loans at given intervals.
 
   
2/15 Review
 
   
2/16 Section 2 Exam
 
   
       
   Section 3 - Logic & Reasoning    
 2/17 Students will be able to make conjectures based on inductive reasoning and find counter-examples.  The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment. 
 CFU:3135.1.4 Use inductive and deductive reasoning strategies to make predictions and valid conclusions based on contextual situations.

 

  3.1-Inductive Reasoning

3.1-Practice Problems
 2/18

 Students will learn to determine truth values of conjunctions and disjunctions as well as construct truth tables. The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment.
 CFU:3135.1.5 Construct truth tables to determine the validity of an argument.

 

  3.2-Logic

3.2-Practice Problems
 2/22  Students will learn to analyze statements in if-then form. Students will also learn to write the converse, inverse and contrapositive of if-then statements. The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment.
CFU:3135.1.4 Use inductive and deductive reasoning strategies to make predictions and valid conclusions based on contextual situations.
 
  3.3-Conditional Statements

3.3-Practice Problems
2/23 Students will learn to use the Laws of Detachment and Syllogism. The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment.
CFU:3135.1.4 Use inductive and deductive reasoning strategies to make predictions and valid conclusions based on contextual situations.
 
  3.4-Deductive Reasoning

3.4-Practice Problems
2/24-2/25  Students will learn to design digital logic gates using NAND, AND, NOR, OR, XAND, and XOR gates. The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment.
CFU:3135.1.4 Use inductive and deductive reasoning strategies to make predictions and valid conclusions based on contextual situations.
 3135.4.5 Develop electrical networks and translate them into Boolean algebra equations.
 
  3.5-Digital Logic

   Students will learn to design digital logic gates using NAND, AND, NOR, OR, XAND, and XOR gates. The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment.
CFU:3135.1.4 Use inductive and deductive reasoning strategies to make predictions and valid conclusions based on contextual situations.
 3135.4.5 Develop electrical networks and translate them into Boolean algebra equations.

 
  3.5a Practice Problems
   Students will learn to design digital logic gates using NAND, AND, NOR, OR, XAND, and XOR gates. The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment.
CFU:3135.1.4 Use inductive and deductive reasoning strategies to make predictions and valid conclusions based on contextual situations.
 3135.4.5 Develop electrical networks and translate them into Boolean algebra equations.

 
  3b-Practice Problems
2/28 Review
 
   
3/1 Section 3 Exam
 
   
       
       
10/5-10/6 Midterm Review
 
   
10/7  3rd & 4th Block Midterm Exams
 
   
10/8  1st & 2nd Block Midterm Exams
 
   
       
  Fall Break
 
   
       
  Section 4 - Graph Theory    
"A Beautiful Mind"
 
   
 3/21 Students will learn to define and draw graphs, paths and circuits. The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment. 
 CFU:3135.4.3 Use vertex-edge graphs to model and solve a variety of problems related to paths, circuits, networks, and relationships among a finite number of objects.
 
   1-Graphs, Paths & Circuits
 3/22 Students will learn to use Euler paths & circuits. The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment.  
CFU:3135.4.3 Use vertex-edge graphs to model and solve a variety of problems related to paths, circuits, networks, and relationships among a finite number of objects.
 
  2-Euler Paths & Circuits
3/23  Students will learn to use Hamilton paths & circuits. The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment. 
CFU:3135.4.3 Use vertex-edge graphs to model and solve a variety of problems related to paths, circuits, networks, and relationships among a finite number of objects.
 
   3-Hamilton Paths & Circuits
3/24  Students will learn to use trees and spanning trees to determine least cost analysis. The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment.
CFU:3135.4.4 The student will apply graphs to conflict-resolution problems, such as map coloring, scheduling, matching, and optimization.
 
   4-Trees
Review
 
   
3/25 Review
 
   
3/28 Section 4 Exam
 
   
       
   Section 5 - Election Theory    
 3/29 Students will learn to use and define the various voting methods commonly used and determine the different outcomes of each. The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment.
 CFU: 3135.1.2 Investigate and describe weighted voting and the results of various election methods. Both very standard and less-known techniques will be studied and compared; these may include approval and preference voting as well as plurality, majority, run-off, sequential run-off, Borda count, and Condorcet winners.
 
  1-Voting Methods
 3/30 Students will learn to define the flaws in common voting methods and determine what constitutes a "fair" election. The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment.
CFU: 3135.1.2 Investigate and describe weighted voting and the results of various election methods. Both very standard and less-known techniques will be studied and compared; these may include approval and preference voting as well as plurality, majority, run-off, sequential run-off, Borda count, and Condorcet winners. 
 
  2-Flaws of Voting
3/31 Students will learn to use common appropriation methods to distribute a limited number of items in a "fair" manner. Students will also learn the flaws in various methods and the groups those methods favor. The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment.
 CFU: 3135.1.3 Use fair division techniques to solve apportionment problems.
 
  3-Apportionment Methods
 4/1  Review
 
   
4/4

 Section 5 Exam
 

 
       
   Section 6 - Probability    
 4/5 Students will learn to determine and calculate empirical probability and see how it is affected by the Law of Large Numbers. The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment.
CFU: 3135.5.6 Apply the Law of Large Numbers to contextual situations.
 
  1-Nature of Probability
 4/6 Students will learn to calculate theoretical probability given a finite set of circustances with specific outcomes. The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment. 
CFU:3135.5.1 Design and interpret simple experiments using tree-diagrams, permutations, and combinations.
 CLE 3135.2.2 Apply appropriate counting techniques in discrete situations.
  
  2-Theoretical Probability
 4/7  Students will learn to determine odds based of specific events. The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment.
CFU:3135.5.1 Design and interpret simple experiments using tree-diagrams, permutations, and combinations.
CLE 3135.2.2 Apply appropriate counting techniques in discrete situations. 
 
  3-Odds
 4/8  Students will learn to use probability to determine expected value of a given event. The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment.
CFU:3135.5.1 Design and interpret simple experiments using tree-diagrams, permutations, and combinations.
CLE 3135.2.2 Apply appropriate counting techniques in discrete situations. 
 
   4-Expected Value
 4/11  Students will learn to use tree diagrams and the counting principle to predict the probability of a given event. The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment.
CFU:3135.5.2 Use reasoning and formulas to solve counting problems in which repetition is not allowed and in which ordering does not matter.
CLE 3135.2.2 Apply appropriate counting techniques in discrete situations. 
 
   5-Tree Diagrams
 4/12  Students will learn to determine probability given AND and OR statements.The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment.
CFU:3135.5.1 Design and interpret simple experiments using tree-diagrams, permutations, and combinations.
CLE 3135.2.2 Apply appropriate counting techniques in discrete situations. 
 
   6-Or & And Problems
 4/13 Students will learn to use determine probability of events given specific conditions. The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment.
CFU:3135.5.2 Use reasoning and formulas to solve counting problems in which repetition is not allowed and in which ordering does not matter
  
   7-Conditional Probabilty
 4/14  Students will learn to use the counting principle to determine probability of a given event and use permutations to determine the number of outcomes possible. The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment.
CFU:3135.5.2 Use reasoning and formulas to solve counting problems in which repetition is not allowed and in which ordering does not matter
  
   8-Counting Principle & Permutations
 4/15  Students will learn to determine probability of multiple events using the counting method. The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment.
CFU:3135.5.2 Use reasoning and formulas to solve counting problems in which repetition is not allowed and in which ordering does not matter
  
   9-Combinations
4/18  Students will learn to apply Pascal's Triangle and the Binomial Theorem to determine probability. The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment.
CFU:3135.5.2 Use reasoning and formulas to solve counting problems in which repetition is not allowed and in which ordering does not matter
3135.5.4 Connect Pascal’s Triangle and probability to solve problems.
3135.5.3 Construct and describe patterns in Pascal’s Triangle.
 
   10-Binomial Probability Formula
 4/19 Review
 
   
 4/20  Section 6 Exam
 
 
       
    Section 7 - Statistics  
 4/21 Students will learn about various sampling techniques commonly used in statistical analysis. The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment. 
CFU: 3135.5.6 Apply the Law of Large Numbers to contextual situations 3135.5.1 Design and interpret simple experiments using tree-diagrams, permutations, and combinations.
 
  1-Sampling Techniques
 4/25  Students will learn about typical misuses and abuses of staistical techniques. The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment. 
CFU: 3135.5.6 Apply the Law of Large Numbers to contextual situations 3135.5.1 Design and interpret simple experiments using tree-diagrams, permutations, and combinations.
 
   2-Misuses of Statistics
 4/26  Students will learn to calculate and understand frequency distributions. The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment. 
CFU: 3135.5.6 Apply the Law of Large Numbers to contextual situations 3135.5.1 Design and interpret simple experiments using tree-diagrams, permutations, and combinations.
 
   3-Frequency Distribution
4/27  Students will learn create and read a typical bell curve. The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment. 
CFU: 3135.5.6 Apply the Law of Large Numbers to contextual situations 3135.5.1 Design and interpret simple experiments using tree-diagrams, permutations, and combinations.
 
   4-Statistical Graphs
4/28 Students will learn to choose and calculate the four varieties of central tendency. The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment. 
CFU: 3135.5.6 Apply the Law of Large Numbers to contextual situations 3135.5.1 Design and interpret simple experiments using tree-diagrams, permutations, and combinations.
 
   5-Measures of Central Tendency
4/29  Students will learn to calculate measures of dispersion. The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment. 
CFU: 3135.5.6 Apply the Law of Large Numbers to contextual situations 3135.5.1 Design and interpret simple experiments using tree-diagrams, permutations, and combinations.
 
  6-Measures of Dispersion
 5/2 Students will learn to create and understand a normal curve. The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment. 
CFU: 3135.5.6 Apply the Law of Large Numbers to contextual situations 3135.5.1 Design and interpret simple experiments using tree-diagrams, permutations, and combinations.
 
  7-Normal Curve
 5/3  Students will learn to create a non-linear prediction equation based on actual experimental data. The teacher will present information using PowerPoint and a white board.  Students will be expected to take notes, ask questions, and practice in class and outside of class.  See Lecture for practice problem assignment. 
CFU: 3135.5.6 Apply the Law of Large Numbers to contextual situations 3135.5.1 Design and interpret simple experiments using tree-diagrams, permutations, and combinations.
 
  8-Linear Correlation & Regression
 5/4  Review  
 5/5

 Section 7 Exam

 

 

 
       
       

 

Lectures are in MS PowerPoint (v10) format. The PowerPoint Vewer or Open Office suite may be freely downloaded.

 

Practice Problems are in PDF format. The 

Adobe Acrobat Viewer is also a free download.