Course Syllabi
Common Syllabi for Mathematics Courses
All sections for any course offered in the calculus & precalculus sequence share a common syllabus, listed below.
Common Syllabus for MATH 100
Chapter 1: Basic Concepts [1.5 Weeks]
• Real numbers
• Order of operations
• Exponents
• Scientific notation
Chapter 2: Equations and Inequalities [2.5 Weeks]
• Solving linear equations
• Story problems including (rate)(time)=distance and mixture problems
• Solving linear inequalities
• Solving equations and inequalities containing absolute values
Chapter 3: Graphs and Functions [2.5 Weeks]
• Graphs, Functions
• Linear Functions, Graphs and story problems
• Slopeintercept form of a linear equation
• Pointslope form of a linear equation
• Algebra of functions
Chapter 4: Systems of Equations and Inequalities [1 Week]
• Solving systems of linear equations in two variables by substitution and by elimination
• Story problems
Chapter 5: Polynomials and Polynomial Functions [3 Weeks]
• Addition, subtraction and multiplication of polynomials
• Division of polynomials (not including synthetic division)
• Remainder theorem
• Factoring methods (as time permits)
Chapter 6: Rational Expressions and Equations [1.5 Weeks]
• Domains, addition, subtraction, multiplication and division of rational expressions
• Work and rate story problems
Chapter 7: Radicals and Complex Numbers [2 Weeks]
• Roots and radicals, rational exponents
• Simplifying radicals
• Adding, subtracting and multiplying radicals (as time permits)
• Rationalizing denominators
Sample Syllabus for MATH 108
Part I  Management Science
Chapter 1: Urban Services [0.5 Weeks]
Euler Circuits, Finding Euler Circuits, Circuits with Reused Edges
Chapter 2: Business Efficiency [1 Week]
Hamiltonian Circuits, Fundamental Principle of Counting, Traveling Salesman Problem, Strategies for Solution, NearestNeighbor Algorithm, SortedEdges Algorithm, MinimumCost Spanning Trees, Kruskal's Algorithm
Chapter 3: Planning and Scheduling [1 Week]
Scheduling Tasks, Assumptions and Goals, ListProcessing Algorithm, When is a Schedule Optimal?, Strange Happenings, CriticalPath Schedules, Independent Tasks, DecreasingTime Lists
Chapter 4: Linear Programming [1 Week]
Mixture Problems, Mixture Problems Having One Resource, One Product and One Resource: Making Skateboards, Common Features of Mixture Problems, Two Products and One Resource: Skateboards and Dolls, Mixture Charts, Resource Constraints, Graphing the Constraints to Form the Feasible Region, Finding the Optimal Production Policy, General Shape of Feasible Regions, The Role of the Profit Formula: Skateboards and Dolls, Setting Minimum Quantities for Products: Skateboards and Dolls, Drawing a Feasible Region When There are Nonzero Minimum Constraints, Finding Corner Points of a Feasible Region Having Nonzero Minimums, Evaluating the Profit Formula at the Corners of a Feasible Region with Nonzero Minimums, Summary of the Pictorial Method, Mixture Problems Having Two Resources, Two Products and Two Resources: Skateboards and Dolls, The Corner Point Principle, Linear Programming: The Wider Picture, Characteristics of Linear Programming Algorithms, The Simplex Method, An Alternative to the Simplex Method
Part III  Voting and Social Choice
Chapter 9: Social Choice: The Impossible Dream [1.5 Weeks]
Elections with Only Two Alternatives, Elections with Three or More Alternatives: Procedures and Problems, Plurality Voting and the Condorcet Winner Criterion, The Borda Count and Independence of Irrelevant Alternatives, Sequential Pairwise Voting and the Pareto Condition, the Hare System and Monotonicity, Insurmountable Difficulties: From Paradox to Impossibility, The Voting Paradox of Condorcet, Impossibility, A Better Approach? Approval Voting
Chapter 11: Weighted Voting Systems [2 Weeks]
How Weighted Voting Works, Notation for Weighted Voting, The Banzhaf Power Index, How to Count Combinations, Equivalent Voting Systems, The ShapleyShubik Power Index, How to Compute the ShapleyShubik Power Index, Comparing the Banzhaf and ShapleyShubik Models
Part IV  Fairness and Game Theory
Chapter 13: Fair Division [1.5 Weeks]
The Adjusted Winner Procedure, The Knaster Inheritance Procedure, DivideandChoose, CakeDivision Procedures: Proportionality, CakeDivision Procedures: The Problem of Envy
Chapter 14: Apportionment [1.5 Weeks]
The Apportionment Problem, The Hamilton Method, Paradoxes of the Hamilton Method, Divisor Methods, The Jefferson Method, Critical Divisors, The Webster Method, The HillHuntington Method, Which Divisor Method is the Best?
Chapter 15: Game Theory: The Mathematics of Competition [as time permits]
TwoPerson TotalConflict Games: Pure Strategies, TwoPerson TotalConflict Games: Mixed Strategies, A Flawed Approach, A Better Idea, PartialConflict Games, Larger Games, Using Game Theory, Solving Games, Practical Applications
Part V  The Digital Revolution
Chapter 16: Identification Numbers [1 Week]
Check digits, the Zip Code, Bar Codes, Encoding Personal Data
Chapter 17: Transmitting Information [1.5 Weeks]
Binary Codes, Encoding with ParityCheck Sums, Data Compression, Cryptography
Note: Instructors may vary the topics covered, and length of time devoted to each. Material shall be selected from:
 Management Science (Street Networks, Visiting Vertices, Planning and Scheduling, Linear Programming)
 Coding Information (Identification Numbers, Transmitting Information)
 Social Choice and Decision Making (Social Choice: The Impossible Dream, Weighted Voting Systems, Fair Division, Apportionment, Game Theory: The Mathematics of Competition)
 On Size and Shape (Growth and Form, Symmetry and Patterns, Tilings), Modeling in Mathematics (Logic and Modeling, Consumer Finance Models)
Common Syllabus for MATH 117
Chapter 1: Relations and Functions
1.1 Sets of Real Numbers and The Cartesian Coordinate Plane
1.2 Relations
1.3 Introduction to Functions
1.4 Function Notation
1.5 Function Arithmetic
1.6 Graphs of Functions
1.7 Transformations
Chapter 2: Linear and Quadratic Functions
2.1 Linear Functions
2.2 Absolute Value Functions
2.3 Quadratic Functions
Chapter 3: Polynomial Functions [2 weeks]
3.1 Graphs of Polynomials
3.2 The Factor Theorem and The Remainder Theorem
3.3 Real Zeros of Polynomials
3.4 Complex Zeros and the Fundamental Theorem of Algebra
Chapter 4: Rational Functions
4.1 Introduction to Rational Functions
4.2 Graphs of Rational Functions
Chapter 5: Further Topics in Functions
5.1 Function Composition
5.2 Inverse Functions
5.3 Other Algebraic Functions
Chapter 7: Hooked on Conics
7.2 Circles
Chapter 8: Systems of Equations and Matrices
8.1 Systems of Linear Equations: Gaussian Elimination
8.2 Systems of NonLinear Equations and Inequalities
Common Syllabus for MATH 118
Chapter 6: Exponential and Logarithmic Functions
Review Section 5.2: Inverse Functions
6.1 Introduction to Exponential and Logarithmic Functions
6.2 Properties of Logarithms
6.3 Exponential Equations and Inequalities
6.4 Logarithmic Equations and Inequalities
6.5 Applications of Exponential and Logarithmic Functions
Chapter 10: Foundations of Trigonometry
10.1 Angles and their Measure
10.2 The Unit Circle: Cosine and Sine
10.3 The Six Circular Functions and Fundamental Identities
10.4 Trigonometric Identities
Review Section 1.7: Transformations
10.5 Graphs of the Trigonometric Functions
10.6 The Inverse Trigonometric Functions
10.7 Trigonometric Equations and Inequalities
Chapter 11: Applications of Trigonometry
11.2 The Law of Sines
11.3 The Law of Cosines
11.4 Polar Coordinates
11.7 Polar Form of Complex Numbers
Common Syllabus for MATH 131
Chapter 1 – A Library of Functions (1.5–2 weeks):
1.1 – Functions and Change
1.2 – Exponential Functions
1.3 – New Functions from Old
 Skip: the subsection on Shifts and Stretches and Odd and Even Symmetry.
 Review of composite and inverse functions, framed in a practical, not merely algebraic, setting.
1.4 – Logarithmic Functions
1.5 – Trigonometric Functions
1.6 – Powers, Polynomials, and Rational Functions
 Skip: the subsection on rational functions (pg 4950).
 Power functions, graph properties for both positive and negative exponents.
 Comparison of longrun behavior of exponentials and polynomials.
1.7 – Introduction to Continuity
 Skip: the majority of the section.
 Understand the graphical viewpoint of continuity. (are there holes, breaks, or jumps in the graph?)
1.8 – Limits
 Skip: the subsection “Definition of Limit” (bottom of pg 58 – 59).
 Skip: the subsection “Definition of Continuity” (see comment on 1.7 above).
 Understand the concept, notation, and properties of limits and onesided limites at a point and limits at infinity.
Chapter 2 – Key Concept – The Derivative (1.5 weeks)
2.1 – How do we measure speed?
2.2 – The Derivative at a Point
 Emphasis on observing what happens to the value of the average rate of change as the interval gets smaller and smaller.
 Emphasis placed on visualizing the derivative as the slope of a tangent.
2.3 – The Derivative Function
 Focus on the conceptual and practical understanding of the derivative.
 Sketch the graph of f ’ given the graph of f.
2.4 – Interpretation of the Derivative
2.5 – The Second Derivative
Chapter 3 – Shortcuts to Differentiation (2.5 weeks)
3.1 – Powers and Polynomials
3.2 – The Exponential Function
 Emphasis on graphical, not epsilondelta, definition of derivative.
 Add: differentiation rule for y=ln(x), from section 3.6.
3.3 – Product and Quotient Rules
3.4 – The Chain Rule
3.5 – The Trigonometric Functions
Chapter 4 – Using the Derivative (3 weeks)
4.1 – Using First and Second Derivatives
4.2 – Optimization
4.3 – Optimization and Modeling
4.4 – Families of Functions and Modeling
4.5 – Applications to Marginality
4.7 – L’Hopital’s Rule, Growth, and Dominance
Chapter 5 – Key Concept – The Definite Integral (2 weeks)
5.1 – How Do We Measure Distance Traveled?
 Skip: accuracy of estimates (pg 277)
5.2 – The Definite Integral
 Approximation using area and interpretation as accumulated change.
5.3 – The Fundamental Theorem and Interpretations
5.4 – Theorems About Definite Integrals
 Finding area between curves; using the definite integral to find an average.
 Skip: the subsection “Comparing Integrals”
Chapter 6 – Constructing Antiderivatives (1 week)
6.1 – Antiderivatives Graphically and Numerically
6.2 – Constructing Antiderivatives Analytically
Common Syllabus for MATH 132
Review of Chapters 5 & 6. Definite and Indefinite Integrals [1.5 to 2 Weeks]
(Prerequisite Material from MATH 131)
5.1 – How Do We Measure Distance Traveled?
Skip: accuracy of estimates (pg 277)
5.2 – The Definite Integral
5.3 – The Fundamental Theorem and Interpretations
5.4 – Theorems About Definite Integrals
properties of definite integrals; area between curves; using the definite integral to find an average
Skip: the subsection “Comparing Integrals”
6.1 – Antiderivatives Graphically and Numerically
6.2 – Constructing Antiderivatives Analytically
Skip: Sections 6.36.4
Chapter 7. Integration [1.5 to 2 Weeks]
7.1 – Integration by Substitution
7.2 – Integration by Parts
7.6 – Improper Integrals
consider only those where limits of integral are infinite
Skip: cases where value of integrand becomes infinite (pp. 398–400)
Skip: Sections 7.3, 7.4, 7.5 & 7.7
Chapter 8. Using the Definite Integral [2 Weeks]
8.6 – Applications to Economics
8.7 – Distribution Functions
8.8 – Probability, Mean, and Median
Skip: Sections 8.1–8.5
Chapter 9. Functions of Several Variables [2.5 to 3 Weeks]
9.1 – Understanding Functions of Two Variables
9.2 – Contour Diagrams
9.3 – Partial Derivatives
9.4 – Computing Partial Derivatives
9.5 – Critical Points and Optimization
9.6 – Constrained Optimization
Chapter 11. Differential Equations [3.5 Weeks]
11.1 – What is a Differential Equation?
11.2 – Slope Fields
11.3 – Euler's Method
11.4 – Separation of Variables
11.5 – Growth and Decay
11.6 – Applications and Modeling
11.7 – The Logistic Model
11.8 – Systems of Differential Equations
11.9 – Analyzing the Phase Plane (time permitting)
Common Syllabus for MATH 161
Chapter 1: Functions and Models [1 week]
1.1 Four Ways to Represent a Function
1.2 Mathematical Models: A Catalog of Essential Functions
1.3 New Functions from Old Functions
1.4 Exponential Functions and Logarithms
1.5 Inverse Functions and Logarithms
Optional: Graphing with calculators, Mathematica, Wolfram Alpha (pp. xxivxxv)
Chapter 2: Limits and Derivatives [2.5 weeks]
2.1 The Tangent and Velocity Problems
2.2 The Limit of a Function
2.3 Calculating Limits Using the Limit Laws
2.4 The Precise Definition of a Limit
2.5 Continuity
2.6 Limits at Infinity; Horizontal Asymptotes
2.7 Derivatives and Rates of Change
2.8 The Derivative as a Function
Chapter 3: Differentiation Rules [3 weeks]
3.1 Derivatives of Polynomials and Exponential Functions
3.2 The Product and Quotient Rules
3.3 Derivatives of Trigonometric Functions
3.4 The Chain Rule
3.5 Implicit Differentiation
3.6 Derivatives of Logarithmic Functions
3.7 Rates of Change in Natural and Social Sciences
3.8 Exponential Growth and Decay
3.9 Related Rates
3.10 Linear Approximations and Differentials
3.11 Optional: Hyperbolic Functions
Chapter 4: Applications of Derivatives [3 weeks]
4.1 Maximum and Minimum Values
4.2 The Mean Value Theorem
4.3 How Derivatives Affect the Shape of a Graph
4.4 Indeterminate Forms and l'Hospital's Rule
4.5 Summary of Curve Sketching
4.6 Optional: Graphing with Calculus and Calculators
4.7 Optimization Problems
4.8 Optional: Newton's Method
4.9 Antiderivatives
Chapter 5: Integrals [2.5 weeks]
5.1 Areas and Distances
5.2 The Definite Integral
5.3 The Fundamental Theory of Calculus
5.4 Indefinite Integrals and the Net Change Theorem
5.5 The Substitution Rule
Common Syllabus for MATH 162
Review. Prerequisite Material from MATH 161 [1 Week]
Rapid review of differentiation rules.
More detailed review of integration (Ch. 5): areas and distances; the definite integral; the fundamental theorem of calculus.
Chapter 6. Applications of Integration [1.5 weeks; 2 weeks if Section 6.4 is covered]
6.1 Area Between Curves
6.2 Volumes
6.3 Volumes by Cylindrical Shells
6.4 Optional: Work ( This Sections could be covered with Chapter 8)
6.5 Average Value of a Function
Chapter 7: Techniques of Integration [3 weeks]
7.1 Integration by Parts
7.2 Trigonometric Integrals
7.3 Trigonometric Substitution
7.4 Integration of Rational Functions by Partial Fractions
7.5 Strategy for Integration
7.6 Integration Using Tables and Computer Algebra Systems
7.7 Approximate Integration
7.8 Improper Integrals
Chapter 11: Infinite Sequences and Series [4 weeks]
11.1 Sequences
11.2 Series
11.3 The Integral Test and Estimates of Sums
11.4 The Comparison Tests
11.5 Alternating Series
11.6 Absolute Convergence and the Ratio and Root Tests
11.7 Strategy for Testing Series
11.8 Power Series
11.9 Representations of Functions as Power Series
11.10 Taylor and Maclauren Series
11.11 Optional: Applications of Taylor Polynomials
Chapter 10: Parametric Equations and Polar Coordinates [11.5 weeks]
10.1 Curves Defined by Parametric Equations
10.2 Optional: Calculus with Parametric Curves
10.3 Polar Coordinates
10.4 Optional: Areas and Lengths in Polar Coordinates
10.5 Optional: Conic Sections
10.6 Optional: COnic Sections in Polar Coordinates
Common Syllabi for Statistics Courses
The statistics courses that share a common syllabus across all sections are listed below.
Common Syllabus for STAT 103

Introduction to Data, Chapters 1 and 2 [1 week]

Types of Data, experiments, sampling

Presenting Data: Organizing and graphing data


Summaries of Center and Variation, Chapter 3 [1 week]

Mean, Median, Standard Deviation, 5 number summary, Percentiles


Probability, Chapter 5 [1 week]

Independence, Conditional Probability


Binomial and Normal Random Variables, Chapter 6 [1 week]

Areas as probability

Normal Approximation to Binomial


Estimation of Population Proportions, Chapter 7 [2 weeks]

Confidence intervals for proportions

Comparing two proportions


Hypothesis Testing for Proportions, Chapter 8 [2 weeks]

Ingredients and logic behind hypothesis testing

Testing one and two proportions


Inference for Population Means, Chapter 9 [2 weeks]

Testing one and two means


Linear Regression Analysis, Chapter 4 [1 week]

Scatter Plots

Correlation


Categorical variables, Chapter 10 (optional, time permitting) [1 week]

One and Twoway tables

χ^{2} tests


Inference for Regression, Chapter 14 (optional, time permitting) [1 week]

Hypothesis testing correlation

Prediction
