01:640:103 Topics in Mathematics for the Liberal Arts
The Complete Exam Bible · Fall 202601:640:103 Overview
- 3 credits
- Fall 2026
- Mathematics
- SAS Core QQ and QR
- Flipped classroom format
Topics in Mathematics for the Liberal Arts is a 3-credit Rutgers course taken mainly by liberal arts and social science majors, with no prerequisite.
- Graded by Two midterms at 20% each and a 30% cumulative final, plus 30% from videos, class work and quizzes.
- Hardest step Choosing the right procedure: the same data give different answers under different methods.
- How to prepare Rework one example per chapter from a blank page and run the built-in check each method has.
- Tools A scientific calculator is needed for homework and exams; phones and algebra calculators are not allowed on exams.
How 01:640:103 is assessed
| Component | Weight | Format |
|---|---|---|
| Pre-Class Videos | 5% | Video lectures with embedded questions before each class |
| In Class Assignments | 10% | Team problem sets handed in at the end of class |
| In Class Quizzes | 15% | A quiz on the day's work at the end of each class |
| Exam 1 | 20% | Midterm listed for 10/7 in the tentative schedule |
| Exam 2 | 20% | Midterm listed for 11/11 in the tentative schedule |
| Final (cumulative) | 30% | Cumulative final, Wednesday, December 16 at 8:00 AM |
The Fall 2026 section syllabus weights the course out of 100 with the six components above. It sets grade thresholds of at least 90% for an A, 80% for at least a B, 70% for at least a C and 60% for at least a D. There are no makeups; two no-questions-asked excuses cover missed quizzes and assignments, and an excused midterm absence shifts that weight onto the matching part of the final.
Assessment structure
Segment widths reproduce the published Fall 2026 weights, which total 100%. The three exams together carry 70%.
Current 01:640:103 dates
| Date | Item | Control |
|---|---|---|
| Tuesday, September 1, 2026 | Semester begins | First day of the Fall 2026 semester. |
| Thursday, September 10, 2026 | Last day to drop without a W | As listed in the section syllabus. |
| 10/7 | Exam 1 | Class 11 in the tentative schedule. |
| 11/11 | Exam 2 | Class 21 in the tentative schedule. |
| Wednesday, December 16, 2026, 8:00 AM | Cumulative final exam | Final (cumulative), 30% of the grade. |
Dates are as published in the Fall 2026 section syllabus and its tentative schedule. Confirm exact deadlines and submission settings in the live LMS.
What 01:640:103 covers
Twelve chapters follow the Fall 2026 class schedule from voting methods to installment loans.
Preference Ballots and Voting Methods
Plurality, Instant Runoff Voting, the Borda Count and Pairwise Comparisons applied to one preference table02Fairness Criteria and Arrow's Impossibility Theorem
The Majority, Condorcet, Monotonicity and Independence of Irrelevant Alternatives criteria, counterexamples and Arrow's theorem03Weighted Voting and the Banzhaf Power Index
Players, weights, quotas and winning coalitions; critical players; Banzhaf power; dictators, veto power and dummies04Shapley-Shubik Power Distribution
Sequential coalitions, pivotal players, N factorial orderings and why listing them becomes impractical05Quotas, Divisors and Hamilton's Method
Standard divisor, standard, lower and upper quotas, the Quota Rule, Hamilton's method and the Alabama paradox06Modified Divisor Methods of Apportionment
Jefferson, Webster and Huntington-Hill: modified divisors, rounding rules, Quota Rule violations and bias07Fair Division of Continuous Goods
Fair shares by each player's own values, Divider-Chooser, Lone Divider with standoffs, and Lone Chooser08Fair Distribution: Sealed Bids and Markers
The Method of Sealed Bids with first and final settlements, and the Method of Markers for many small items09Hamilton Circuits and the Traveling Salesman Problem
Weighted graphs, Hamilton circuits, (N − 1)! counting, Brute Force, Nearest Neighbor, Repetitive Nearest Neighbor and Cheapest Link10Trees, Networks and Kruskal's Algorithm
Connected graphs, trees, spanning trees, the V − 1 edge count, redundancy and minimum spanning trees by Kruskal11Growth Factors and Compound Interest
Growth and decline factors, successive percentage changes, compound interest and FV = PV(1 + i)^n12Compounding Frequency, APY, Annuities and Loans
Periodic rates, APR versus APY, what a regular savings plan grows to, and installment loan paymentsIt studies places where mathematics is applied concretely: how elections are decided, how much power a voter really holds, how seats are apportioned, how goods are divided fairly, how to plan efficient routes and networks, and how money and populations grow.
This guide follows the Fall 2026 flipped section's class schedule chapter by chapter.
The voting and power block
The course begins with preference ballots and four voting methods, Plurality, Instant Runoff Voting, the Borda Count and Pairwise Comparisons, and then judges them with the Majority, Condorcet, Monotonicity and Independence of Irrelevant Alternatives criteria, ending with Arrow's impossibility theorem.
The power classes measure how much influence each player in a weighted voting system really has, first by the Banzhaf index and then by the Shapley-Shubik index.
Exam 1 follows these two topics in the tentative schedule.
The apportionment and fair division block
Apportionment shares indivisible seats in proportion to population: standard divisors and quotas, Hamilton's method and the Alabama paradox, then the divisor methods of Jefferson, Webster and Huntington-Hill.
Fair division gives each player a share worth at least one Nth of the goods by that player's own values, with Divider-Chooser, Lone Divider and Lone Chooser for land or time and the Methods of Sealed Bids and Markers for indivisible items.
Exam 2 follows this block.
Graphs and finance
The last classes cover Hamilton circuits and the Traveling Salesman Problem, where only Brute Force is guaranteed optimal and Nearest Neighbor and Cheapest Link trade accuracy for speed, then trees and Kruskal's Algorithm, which is both efficient and optimal.
The course closes with growth factors, compound interest, APR and APY, savings annuities and installment loans.
These two topics are examined for the first time on the cumulative final.
How to use this guide
Every chapter works complete examples with original numbers, so you can check each step with a calculator, and every method comes with a built-in check: Borda totals, power indices that sum to one, seats that sum to the house size, settlements where cash in equals cash out.
Work a chapter's example without looking, then change one number and predict what moves before recomputing.
Three methods, one small election
- 2Plurality: X has 10 first choices, Z 8 and Y 5, so X wins without a majority (12 needed).
- 2Instant Runoff: Y is eliminated; its 5 ballots go to Z, which beats X 13 to 10.
- 2Borda: X 10×3 + 13×1 = 43, Y 10×2 + 8×2 + 5×3 = 51, Z 10×1 + 8×3 + 5×2 = 44; total 138 = 6 × 23.
- 2Head to head Y beats X 13 to 10 and Z 15 to 8, so Y is the Condorcet candidate.
Key terms
- Voting method
- A voting method is a rule that turns a table of preference ballots into a winner and, when extended, a full ranking.
- Majority candidate
- A majority candidate is ranked first on over half of the ballots.
- Condorcet Criterion
- The Condorcet Criterion says a candidate who beats every rival head to head should win.
- Weighted voting system
- A weighted voting system gives players different numbers of votes and passes motions that reach a quota.
- Banzhaf power index
- The Banzhaf power index measures a player's share of all critical appearances in winning coalitions.
- Standard divisor
- The standard divisor is how many people one seat stands for on average: population total over seats.
- Quota Rule
- The Quota Rule asks that every state receive its lower or its upper quota of seats.
- Fair share
- A fair share is a portion worth at least one Nth of the goods to the player who receives it.
- Minimum spanning tree
- A minimum spanning tree connects every vertex with the least possible total edge weight and no circuits.
- Annual percentage yield
- The annual percentage yield is the effective yearly growth rate once compounding within the year is counted.
01:640:103 FAQ
What topics does Topics in Mathematics for the Liberal Arts cover?
The mathematics of voting, measuring power in weighted voting, apportionment, fair division of continuous and discrete goods, Hamilton circuits and spanning trees, and growth and finance, including compound interest, annuities and loans, in that order across the semester.
How much is the final exam worth, and is it cumulative?
The final is worth 30% of the course grade and is cumulative. The Fall 2026 section syllabus lists it for Wednesday, December 16 at 8:00 AM, and the two midterms are worth 20% each.
What score do I need for an A?
The syllabus sets an A at a course score of at least 90%. At least 80% guarantees at least a B, at least 70% at least a C, and at least 60% at least a D.
Which calculator can I use on exams?
A scientific calculator is needed for homework and exams. Devices with typewriter keyboards, built-in computer algebra or wifi, including cellphones, are not permitted during exams, so practise with the calculator you will bring.
What happens if I miss a quiz or an exam?
There are no makeups, but two no-questions-asked excuses cover missed quizzes and assignments. A midterm absence excused for truly compelling reasons is not made up; instead the matching part of the final counts more heavily.
How does the flipped format work each week?
Before class you watch video lectures and answer their embedded questions. In class you work homework-level problems in a team, hand in the written work at the end, and finish with a quiz on that day's material.
What is the best way to study for this course?
Practise procedures on fresh numbers rather than rereading solutions. For each method, work one example unaided, then run its check, such as totals that must match, before moving to the next topic.
How to study for the exam
Treat every topic as a procedure with a check. Before each exam, rework one example per chapter in that block from a blank page, name the method first, show the table the method builds, and confirm the check: Borda points, power indices summing to one, seats matching the house size, or cash in equal to cash out. For the final, add graphs and finance, which appear on no midterm.
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