Intended to broaden students' understanding of methods, history and applications of mathematics. Logic, mathematical proofs, numeration systems, modular arithmetic, coordinate geometry and graphing, elementary probability and statistics, linear programming and financial math.
64.000-72.000 Total Hours
Total Hours
128.000-144.000 Total Hours
64.000-72.000 Total Hours
Prerequisite: MATH 107 or equivalent based on SBCC's Assessment Center placement via multiple measures. Prerequisite or Corequisite: None Concurrent Corequisite: None Course Advisories: None Limitation on Enrollment: None
Course Objectives:
Translate propositions and arguments into symbolic form and determine their equivalence and/or validity by using truth tables or another algorithmic method
Identify common fallacies in arguments.
Provide counterexamples for invalid arguments and models demonstrating the independence of propositions from simple axiomatic systems.
Perform simple Boolean operations on sets
Express/define sets with set-builder (intensional) notation.
Identify/distinguish the different kinds of numbers (e.g., integers, real numbers) and their historical motivations.
Identify/distinguish countable and uncountable sets, and state Cantor’s Continuum Question.
Translate between base 10 and other bases as well as between base 10 and Mayan and Roman numerals. ??
Perform arithmetic operations in bases other than 10.
Prime-factor numbers; use prime-factorization to determine the GCD and LCM of sets of two or more numbers.
Solve simple divisibility problems using congruences.
State some open problems in Number Theory.
Solve simple counting problems using the Fundamental Principle of Counting, permutations, and combinations
Student Learning Outcomes
MATH114 SLO1 - Apply the rules of probability and combinatorics to solve problems and interpret their results.
MATH114 SLO2 - Explain and describe geometric concepts
MATH114 SLO3 - Analyze arguments and formulate valid conclusions using inductive and deductive reasoning
MATH114 SLO4 - Identify and analyze the implications and consequences of various financial decisions concerning borrowing and investing money.
Set Theory
Well-defined sets, the empty set, set notation, subsets, set operations, Cartesian products, cardinality and one-to-one correspondence.
Subsets versus proper subsets, equivalent versus equal sets.
Venn diagrams: representations of sets, verification of set relationships, use in applications such as survey problems.
Real numbers and their subsets with an emphasis on the types of numbers and not on arithmetic operations; rational and irrational numbers; properties of the real numbers.
Infinite sets, transfinite numbers, and Cantor's influence on these ideas.
Logic
Translation of compound statements into symbolic statements.
Creation of truth tables for compound statements using logical connectives.
Tautologies and logically equivalent statements including the use of DeMorgan's laws.
Converse, contrapositive, and inverse of a given conditional statement; equivalence of these forms.
Determination of the validity of an argument using truth tables, Venn diagrams, or by recognizing valid forms.
Logical symbols in applications such as circuits.
Mathematical Modeling
Modeling of various real-world situations with an emphasis on linear, quadratic, exponential and logarithmic functions.
Use of models to analyze and make predictions about real-world situations.
Determination of reasonable domains in specific applications and of the validity of quantitative results.
Characteristics and trends of various mathematical models; identification or appropriate models to fit various real-life situations.
Probability and Statistics
Randomness, populations, samples, sample spaces, and events.
Probability calculation using counting methods including the basic counting law, tree diagrams, Venn diagrams, combinations, and permutations.
Mutually exclusive and independent events.
Compound and conditional probabilities.
Measures of central tendency (mean, median, mode) and dispersion (variance, standard deviation).
Frequency distributions, histograms, and pie charts.
Probability calculation using the normal curve, the Z statistic, and probability tables.
The Mathematics of Finance
Simple and compound interest formulas, annuities, and amortized loans.
Axiomatic systems, Euclidean geometry, and non-Euclidean geometries.
Methods of Instruction
Discussion
Distance Education
Lecture
Lecture is the primary activity to be used, along with student problem-solving. Students are required to work outside of class on assigned exercises as well as on supplementary reading from the text and other source material.
Compare the interest due on a $1000 loan at 12% after one year when it is compounded annually, quarterly, monthly, daily and continuously.
A. Appropriate Readings: Students are required to read assigned chapters in texts. Outside readings are generally not required.
B. Writing Assignments: Students must work assigned mathematical problems requiring the manipulation of abstract symbols.
C. Appropriate Outside Assignments: Students will be expected to spend a sufficient amount of time outside of class to practice techniques taught during class time, read assigned materials, and complete frequent homework assignments.
D. Appropriate Assignments that Demonstrate Critical Thinking: Students must demonstrate mathematical skills such as equation solving and graphing which involve analyzing information, recognizing concepts in new contexts, and drawing analogies.
A student's grade will be based on multiple measures of performance in the solving of algebra problems, preparation and analysis of graphs. Such measures will include at least three exams and a comprehensive final examination requiring demonstrations of problem-solving skills. In addition, instructors may make use of quizzes, written homework assignments, or other appropriate means to judge a student's dexterity with algebra skills and familiarity with mathematical vocabulary.
Instructors are required to provide students, in writing, with a course syllabus in accordance with district policy, which will include the specific procedures by which students will be evaluated. These procedures must be consistent with the objectives and course content stated above.
Math in Our WorldSabecki, David, Cengage Learning Academic, 2014