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
All sections and chapters referred to are from Precalculus: A Prelude to Calculus
Chapter 1: Functions and Their Graphs [3 weeks]
1.1  Functions
1.2  The Coordinate Plane and Graphs
1.3  Function Transformations and Graphs
1.4  Composition of Functions
1.5  Inverse Functions
1.6  A Graphical Approach to Inverse Functions
Chapter 2: Linear, Quadratic, Polynomial, and Rational Functions [3.5 weeks]
2.1  Lines and Linear Function
2.2  Quadratic Functions and Conics (material on ellipses and hyperbolas is optional)
Appendix A: Area
2.3  Exponents
2.4  Polynomials
2.5  Rational Functions
Chapter 3: Exponential Functions, Logarithms, and e [4.5 weeks]
3.1  Logarithms as Inverses of Exponential Functions
3.2  Applications of the Power Rule for Logarithms
3.3  Applications of the Product and Quotient Rules for Logarithms
3.4  Exponential Growth
3.5  e and the Natural Logarithm (skip entirely pages 278283)
3.6  Approximations and Area with e and ln
3.7  Exponential Growth Revisited
Chapter 8: Systems of Linear Equations [1 week]
8.1  Solving Systems of Linear Equations
8.2  Matrices (skip entirely)
Syllabus leaves 2 weeks for tests, optional material, etc.
Common Syllabus for MATH 118
All sections and chapters referred to are from Precalculus: A Prelude to Calculus
Review of material from Math 117 [1.5 weeks]
Material from Sections 1.1, 1.2, 1.4, 1.5, 1.6, 2.3, and Chapter 3
Chapter 4: Trigonometric Functions [2.5 weeks]
4.1  The Unit Circle
4.2  Radians
4.3  Cosine and Sine
4.4  More Trigonometric Functions
4.5  Trigonometry in Right Triangles
4.6  Trigonometric Identities
Chapter 5: Trigonometric Algebra and Geometry [3 weeks]
5.1  Inverse Trigonometric Functions
5.2  Inverse Trigonometric Identities (optional)
5.3  Using Trigonometry to Compute Area
5.4  The Law of Sines and the Law of Cosines
5.5  DoubleAngle and HalfAngle Formulas
5.6  Addition and Subtraction Formulas
Chapter 6: Applications of Trigonometry [3 weeks]
Briefly review material from Chapter 1.3: Function Transformations and Graphs
6.1  Transformations of Trigonometric Functions
6.2  Polar Coordinates
6.3  Vectors (skip entirely)
6.4  Complex Numbers
6.5  The Complex Plane
Appendix B: Parametric Curves (optional)
Chapter 7: Sequences, Series, and Limits [2 week]
7.1  Sequences
7.2  Series
7.3  Limits
Syllabus leaves 2 weeks for tests, projects, etc.
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 [1 week]
Functions and their graphs: identifying functions, mathematical models.
Combining functions; shifting and scaling graphs.
Graphing with calculators and computers (introduction to Mathematica).
Exponential functions.
Inverse functions and logarithms.
Optional: Hyperbolic functions.
Chapter 2. Limits and Continuity [1.5 weeks]
Rates of change and tangents to curves.
Calculating limits using the limit laws.
The precise definition of a limit.
Onesided limits, continuity.
Limits involving infinity: limits at infinity, infinite limits; asymptotes of graphs.
Chapter 3. Differentiation [4 weeks]
Tangents and the derivative at a point.
The derivative as a function.
Differentiation rules: for polynomials and exponentials; for products and quotients.
The derivative as a rate of change.
Derivatives of trigonometric functions.
The chain rule.
Implicit Differentiation.
Derivatives of inverse functions and logarithms.
Inverse trigonometric functions.
Related Rates.
Linearization and differentials.
Additional material (§§11.1, 11.2): parametric equations and their derivatives.
Derivatives of Hyperbolic Functions.
Chapter 4. Applications of Derivatives [3 weeks]
Extreme values of functions.
Rolle’s theorem and the mean value theorem.
Monotonic functions and the first derivative test.
Concavity and curve sketching.
Applied optimization problems.
Indeterminate forms and l’Hopital’s rule.
Newton’s Method.
Antiderivatives.
Chapter 5. Integration [4 weeks]
Area estimates with finite sums.
Sigma notation and limits of finite sums.
The definite integral.
The fundamental theorem of calculus.
Indefinite integrals and the substitution method.
Substitution and area between curves.
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 Definite Integrals [23 weeks]
Using integrals to calculate volumes of solids, length of curves, surface areas of solids of revolution.
Applications to physics (instructor to select from moments and center of mass, work, fluid pressures and forces).
Chapter 7. Integrals of Transcendental Functions [1 week]
The logarithm defined as an integral.
Exponential functions and hyperbolic functions.
Chapter 8. Techniques of Integration [3 weeks]
Basic integration formulas; integration by parts.
Integration of rational functions by partial fractions; trigonometric integrals; trigonometric substitution.
Integration using tables and computer algebra systems; approximate integration.
Improper integrals of Type I and Type II; comparison tests for convergence of improper integrals.
Chapter 10. Infinite Sequences and Series [4 weeks]
Numerical sequences and series; integral test and estimates of sums; comparison tests.
The ratio and root tests.
Alternating series; absolute and conditional convergence.
Strategy for testing convergence of series; the rearrangement theorem for absolutely convergent series.
Power series; representations of functions as power series.
Taylor and Maclaurin series.
Binomial series; applications of Taylor polynomials; complex numbers and Euler's identity.
Chapter 11. Conic Sections and Polar Coordinates [12 weeks]
Rotations, polar coordinates; arc length in polar coordinates.
Conic sections and quadratic equations.
Chapter 9. First Order Differential Equations [as time permits]
Optional: Selected topics from §§ 1 & 2. Solutions, slope fields, Euler's method, firstorder linear equations.
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
