Liberal Arts Mathematics I

Assignments Table


If you have not yet done so, you need to read the information in the Initial Information document and work through the Orientation and Startup to which that document refers you.

It is necessary to have done so in order to understand this page and to use it properly.


You have been introduced to this course and this page in the Orientation and Startup.

The links below will take you to the various sources of information.


How to Complete Assignments

You will have been introduced to the use of Open QA and Open Query documents and to the use of the DVDs in your Startup and Orientation, which should have been completed by the end of the first week of the class.  Your text is very well-written and accessible.  Using these resources, you are expected to simply begin working through the course, following the posted schedule.  You are welcome to work ahead of the schedule.

Assignments are numbered 01 - 29.  The suggested pattern of activities for each assignments is as follows:

 


Important note:  Videos are posted at the link entitled 'videos' on your homepage.  That link is just underneath the links to the Assignments and Brief Assignments pages.  For your convenience it is also given below:


 

Table of Assignments and Specific Objectives

Module 1:  Chapter 2

Chapter 2 Test to be taken within about a week of completing Chapter 2 assingments; see Due Dates Document

Assignment 01 Open QA Text Section 2.1 Open Query  
Objectives:  Know and apply the following to answer questions and solve problems.
  1. Correctly recognize and apply standard symbols and terminology for describing and denoting finite and infinite sets, inclusion in a set, set equality, cardinality.
  2. Correctly interpret and properly represent sets using set-builder notation.
Assignment 02 Open QA Text Section 2.2 Open Query  
Objectives:  Know and apply the following to answer questions and solve problems.
  1. Correctly recognize and apply standard symbols and terminology for describing and denoting subsets, proper subset, complement of a set.
  2. Represent sets and their relationships using Venn diagrams.
Assignment 03 Open QA Text Section 2.3 Open Query  
Objectives:  Know and apply the following to answer questions and solve problems.
  1. Correctly recognize and apply standard symbols and terminology for describing and denoting set union, intersection, difference, equality of sets and cartesian products.
  2. Describe sets in words, and given a description of a set in words write the set in mathematical notation.
  3. Correctly shade Venn diagrams representing various set operations.
Assignment 04 Open QA Text Section 2.4 Open Query  
Objectives:  Know and apply the following to answer questions and solve problems.
  1. State and apply deMorgan's Laws, and explain those laws both in words and using Venn diagrams.
  2. State the cardinal number formula, and explain it in words or with Venn diagrams.
  3. Analyze data from surveys, tables or reports when given sufficient information to reason out the cardinalities of all 8 regions into which 3 sets generally divide the universal set.

 

Assignment 05 Open QA Text Section 2.5

(alternatively extension labeled 'Infinite Sets and their Cardinalities')

Open Query Complete Ch 2 Test within a week of completing Ch 2 assignments
Objectives:  Know and apply the following to answer questions and solve problems.
  1. Where it is possible to do so, define one-to-one correspondences between sets; where this is not possible show why.
  2. State and apply the meaning of aleph-null.

Module 2:  Chapter 1

Chapter 1 Test to be taken within about a week of completing Chapter 1 assingments; see Due Dates Document

Assignment 06 Open QA Text Section 1.1 Open Query  
Objectives:  Know and apply the following to answer questions and solve problems.
  1. Correctly distinguish between inductive and deductive arguments.
  2. Solve problems using inductive and deductive reasoning.
Assignment 07 Open QA Text Section 1.2 Open Query  
Objectives:  Know and apply the following to answer questions and solve problems.
  1. Apply inductive reasoning to solve problems involving number patterns and figurate numbers.

 

Assignment 08 Open QA Text Section 1.3 Open Query  
Objectives:  Know and apply the following to answer questions and solve problems.
  • State and apply to the solution of problems a variety of problem-solving strategies.
Assignment 11 Open QA Text Section 1.4 Open Query Complete Ch 1 Test within a week of completing Ch 1 assignments
Objectives:  Know and apply the following to answer questions and solve problems.
  1. Construct and interpret pie graphs, histograms, point graphs and line graphs.
  2. Quickly approximate the results of arithmetic calculations using reasonable estimates.

Module 3:  Chapter 3

Chapter 3 Test to be taken within about a week of completing Chapter 3 assingments; see Due Dates Document

Assignment 12 Open QA Text Section 3.1 Open Query  
Objectives:  Know and apply the following to answer questions and solve problems.
  1. State definition of the word 'statement' and distinguish between statements and non-statements.
  2. Symbolize compound statements formed by conjunctions, disjunctions and negations.
  3. Identify and apply universal and existential quantifiers.
  4. Negate statements formed from universal ('all do' or 'all do not') or existential ('some do' or 'some do not') quantifiers.
  5. State the definitions of real numbers, integers, whole numbers, counting numbers, rational numbers, and irrational numbers, and the relationships among these sets.
Assignment 13 Open QA Text Section 3.2 Open Query  
Objectives:  Know and apply the following to answer questions and solve problems.
  1. Apply the rules for determining the truth values of negations, conjunctions and disjunctions.
  2. Construct truth tables, in which each column can be evaluated by reference to at most two other columns, to determine the truth values of compound statements formed by negations, conjunctions and disjunctions of simple statements.
  3. Validate deMorgan's Laws using truth tables.
  4. Symbolize compound verbal statements in terms of simple statements, and evaluate the truth values of those statements.
Assignment 14 Open QA Text Section 3.3 Open Query  
Objectives
  1. State and be able to explain the reasons for the rule used to evaluate the truth value of a conditional.
  2. Translate a verbal or symbolic conditional into a disjunction, and negate it.
  3. Use truth tables, in which each column can be evaluated by reference to at most two other columns, to determine the truth values of compound statements formed by negations, conjunctions, conditionals and disjunctions of simple statements.
  4. Given a circuit translate it as a compound logical statement, and vice versa.
  5. Evaluate a compound statement by evaluating the corresponding circuit.
Assignment 15 Open QA Text Section 3.4 Open Query  
Objectives
  1. State and apply the definitions of the converse, inverse and contrapositive of a conditional.
  2. Evaluate the relative truth values of a statement and its converse, inverse and contrapositive.
  3. State, interpret and apply alternative verbal forms of the conditional.
  4. Apply the converse, inverse and contrapositive to write equivalent forms of conditional statements.
  5. State and apply the definition of the biconditional.
  6. State and apply the definition of 'consistent' and 'contrary'.
Assignment 16 Open QA Text Section 3.5 Open Query  
Objectives:  Know and apply the following to answer questions and solve problems.
  1. Use Euler diagrams to represent conditionals, negations and quantified statements.
  2. Use Euler diagrams to represent and evaluate arguments.
Assignment 17 Open QA Text Section 3.6 Open Query Complete Ch 3 Test within a week of completing Ch 3 assignments
Objectives:  Know and apply the following to answer questions and solve problems.
  1. Given an argument involving compound statements, write the argument as a conditional, evaluate the conditional and determine the validity of the argument.
  2. Given a set of premises, use modus ponens, modus tollens, disjunctive syllogism and/or transitivity, as appropriate, to draw a valid conclusion.  (It is not required that you know the terms ' modus ponens', 'modus tollens', or 'disjunctive syllogism'.  You should know the term 'transitivity' and recognize when you are using it.  It's not required but it's a good idea to understand the meaning of 'direct argument' (vernacular for 'modus ponens') and 'argument by contradiction' (vernacular for 'modus tollens').) 

Module 4:  Chapter 4

Chapter 4 Test to be taken within about a week of completing Chapter 4 assingments; see Due Dates Document

Assignment 18 Open QA Text Section 4.1 Open Query  
Objectives:  Know and apply the following to answer questions and solve problems.
  1. Given a table defining the symbols for Egyptian, Roman or Chinese numeration systems, write a given Hindu-Arabic number in the notation of that system, and write a number in any of those systems in Hindu-Arabic form.
  2. Perform addition or subtraction using Egyptian symbols (as opposed, for example, to translating the Egyptian symbols to Hindu-Arabic notation and doing the arithmetic in the usual fashion before translating back to Egyptian symbols).
  3. Perform multiplication using the Egyptian algorithm.
Assignment 19 Open QA Text Section 4.2 Open Query  
Objectives:  Know and apply the following to answer questions and solve problems.
  1. Given a table defining the symbols for Babylonian, Mayan or Greek numeration systems, write a given Hindu-Arabic number in the notation of that system, and write a number in any of those systems in Hindu-Arabic form.
Assignment 20 Open QA Text Section 4.3 Open Query  
Objectives:  Know and apply the following to answer questions and solve problems.
  1. Interpret numbers represented on an abacus.
  2. Apply the Russian Peasant Method for multiplication.
  3. Apply the above to solve problems.
  4. Convert a base-10 number to another specified base (including hexadecimal).
Assignment 21 Open QA Text Section 4.4 Open Query  
Objectives:  Know and apply the following to answer questions and solve problems.
  1. Convert a number in a specified base (including hexadecimal) to a base-10 number.
  2. Convert between binary and hexadecimal representations of a number.
Assignment 22 Open QA Text Section 4.5

(alternatively listed as 'Extension:  Modular Systems')

Open Query  
Objectives:  Know and apply the following to answer questions and solve problems.
  1. Perform 'clock arithmetic' on a clock with a given number of hours.
  2. Perform modular arithmetic for a given modulus.

Module 5:  Chapter 5

Chapter 5 Test to be taken within about a week of completing Chapter 5 assingments; see Due Dates Document

Assignment 23 Open QA Text Section 5.1 Open Query Complete Ch 4 Test within a week of completing Ch 4 assignments
Objectives:  Know and apply the following to answer questions and solve problems.
  1. State and apply the definitions of prime and composite numbers.
  2. Apply divisibility tests for divisibility by 2, 3, 4, 5, 6, 8, 9, 10 and 12 to a given number.
  3. Calculate the prime factorization of a given number.
  4. Calculate all the natural-number factors of a given number.
  5. Apply the Sieve of Erasthones to find the primes up to number n, where n is a specified natural number.
Assignment 24 Open QA Text Section 5.2 Open Query  
Objectives:  Know and apply the following to answer questions and solve problems.
  • Explain how we can prove that there are infinitely many primes.
  • Check the Mersenne numbers M_n = 2^n - 1 for values of n up through 10 and identify corresponding Mersenne primes.
  • Generate Fermat numbers 2^(2^n) + 1 for values of n up to 3, and identify those which are prime.
Assignment 25 Open QA Text Section 5.3 Open Query  
Objectives:  Know and apply the following to answer questions and solve problems.
  1. Explain how to prove that there are infinitely many primes.
  2. Check the Mersenne numbers M_n = 2^n - 1 for values of n up through 10 and identify corresponding Mersenne primes.
  3. Generate Fermat numbers 2^(2^n) + 1 for values of n up to 3, and identify those which are prime.
  4. Identify a given number as perfect, deficient or abundant.
  5. List the perfect numbers less than 100.
  6. Verify Goldbach's Conjecture for a given number by showing how it is the sum of two primes.
Assignment 26 Open QA Text Section 5.4 Open Query  
Objectives:  Know and apply the following to answer questions and solve problems. 
  1. Verify whether two given numbers are amicable.
  2. Identify twin primes up to 100.
  3. State Fermat's Last Theorem and explain how it is related to the Pythagorean Theorem.
  4. Find the greatest common factor or least common multiple of two or more given numbers based on their prime factorizations.
  5. Find the greatest common factor or least common multiple of two or more given using division by primes.
  6. Find the greatest common factor of two numbers using the Euclidean Algorithm
Assignment 27 Open QA Text Section 5.5 Open Query Complete Ch 5 Test by the end of the term
Objectives:  Know and apply the following to answer questions and solve problems.
  1. State and identify the pattern of the Fibonacci sequence.
  2. State and apply the recursion formula for the Fibonacci sequence.
  3. Prove and/or verify stated characteristic of the Fibonacci sequence.
  4. Demonstrate how the successive ratios of the Fibonacci sequence approach the golden ratio.

Module 6:  Chapter 7

Chapter 7 Test to be taken by the end of the Exam Period; see VHCC College Calendar and Due Dates Document

Assignment 28 Open QA Text Section 7.1 and 7.2 Open Query  
Objectives:  Know and apply the following to answer questions and solve problems.
  1. State the properties of equality and use them to solve linear equations.
  2. Write the linear equation that models a given linear phenomenon.
  3. Apply the above to solve problems, especially problems involving geometrical quantities, mixtures, interest and rates.
Assignment 29 Open QA Text Section 7.3 Open Query Complete Ch 7 Test by the end of the term
Objectives:  Know and apply the following to answer questions and solve problems.
  1. Write and reduce to lowest terms the ratio of two given quantities.
  2. Correctly apply the word 'per' to the ratio of two quantities.
  3. Write and solve statements of proportion.
  4. State the forms of the statements of direct variation, inverse variation, and variation with a power.
  5. Apply direct variation to solve problems.
  6. Write equations for, apply and solve problems related to joint or combined variation.

 

Standard Assignment from Text Section:

Read the text and work on paper every problem at the end of the section which is numbered as a multiple of 3 or 5 (multiples of 3 would be 3, 6, 9, 12, ...; multiples of 5 would be 5, 10, 15,...; you should therefore work problems 3, 5, 6, 9, 10, 12, 15, 18, 20, 21, ...).