QRC Resource Directory
Quantitative Resource Center, Lawrence University. Version 0.2, updated 2026-10-03. Free, vetted resources for quantitative work. Entries marked ★ are QRC picks.
Start here at Lawrence
I want a person to help me, or I need to take the math placement. Free campus services. These are the first stop when you want a person rather than a link.
- ★ QRC drop-in tutoring (Lawrence University)
Peer tutors for 100- and 200-level math and Q-requirement courses. No appointment needed. Bring your work and a specific question if you can.
Start: Mudd Library, 2nd floor, Sunday–Thursday evenings. Check the tutor board for who is on tonight. - ★ ALEKS math placement (Lawrence University, Department of Mathematics)
Required before math or physics courses. Scores of 75+ place into calculus (MATH 140), 45–74 into MATH 103, and below 45 into MATH 102. After your first attempt you get personalized ALEKS learning modules.
Start: To retake the proctored test, wait 48 hours and complete at least 5 hours in the learning modules. - Course tutors through Navigate (Lawrence University, Center for Academic Success)
One-on-one and small-group content tutoring for specific courses, plus writing, oral communication, and multilingual support. Request a tutor in MyLU Navigate or ask your instructor.
Start: Check your course's Canvas site or syllabus for an assigned tutor first. - Center for Academic Success (Lawrence University)
Success coaching on time, motivation, and study habits, academic skills workshops, and peer tutoring programs. A good next step when the problem is bigger than one course.
Start: Mudd Library, 2nd floor, weekdays 8–5. Book a coaching meeting from the CAS page. - Mudd Library (Lawrence University)
Research help, data and systems librarianship, course reserves, and quiet study space. The QRC and CAS are on the library's 2nd floor.
Start: Ask at the main desk for help finding data or a statistics text. - [Used at Lawrence] OpenStax textbook library (OpenStax, Rice University)
Free, peer-reviewed textbooks in math, statistics, the sciences, economics, and more. Lawrence's intro math courses use OpenStax texts, so your assigned book may already be free here as a web page, PDF, or app.
Start: Check your syllabus for the book title, then find it by subject.
Foundations and catching up
I'm rusty on fractions, algebra, or the basics, or I'm preparing for ALEKS. Arithmetic through intermediate algebra. Matches MATH 102 and the early part of MATH 103.
- ★ Khan Academy (Khan Academy (nonprofit))
Short videos and unlimited practice with instant feedback, arranged in mastery units. Good for filling a specific gap (negative numbers, fractions, factoring) without redoing a whole course.
Start: Use a unit test or course challenge to find your gaps, then work only those skills. - ★ [Used at Lawrence] Prealgebra 2e (OpenStax, Rice University)
A complete, peer-reviewed text on whole numbers, fractions, decimals, percents, and an introduction to algebra. Every section has worked examples followed by "try it" problems with answers.
Start: The fractions and decimals chapters are the most-used review. - ★ Paul's Online Math Notes (Paul Dawkins, Lamar University)
Clear class notes with many worked examples for algebra through differential equations, with practice problems and solutions. Students often find these easier to read than their textbook. It also has review pages on algebra and trig for calculus students.
Start: For a quick refresher, try the Algebra/Trig Review under Extras, or the cheat sheets. - [Used at Lawrence] Intermediate Algebra 2e (OpenStax, Rice University)
Linear equations, systems, polynomials, rational expressions, radicals, and quadratics, with lots of practice. A good bridge from MATH 102 into MATH 103.
Start: Use the chapter review exercises as a self-check before an exam. - Algebra, trig, and calculus cheat sheets (Paul Dawkins, Lamar University)
Printable reference sheets: algebra rules, common errors, trig identities, and derivative and integral tables. The "common algebra errors" sheet is useful before any exam.
Start: Print the algebra sheet for your notebook.
Functions, precalculus, and trigonometry
I'm in MATH 103 or getting ready for calculus. Functions, graphs, exponentials and logarithms, and trigonometry.
- ★ [Used at Lawrence] Precalculus 2e (OpenStax, Rice University)
Functions, polynomial and rational functions, exponentials and logarithms, trigonometry, and conics. Clean examples and many practice problems with odd answers in the back.
Start: Chapter 1 (functions) and chapter 4 (exponential and logarithmic functions) match the core of MATH 103. - ★ Paul's Online Notes: Algebra (Paul Dawkins, Lamar University)
Clear notes with many worked examples on equations, functions, polynomial and rational functions, exponentials and logarithms, and systems. Each section has practice problems with full solutions.
Start: The Exponential and Logarithm Functions chapter is a common MATH 103 rescue. - Algebra, trig, and calculus cheat sheets (Paul Dawkins, Lamar University)
Printable reference sheets: algebra rules, common errors, trig identities, and derivative and integral tables. The "common algebra errors" sheet is useful before any exam.
Start: Print the algebra sheet for your notebook. - [Used at Lawrence] College Algebra 2e (OpenStax, Rice University)
The algebra half of precalculus without trigonometry: equations, inequalities, functions, and systems.
Start: Use it when your course is algebra-heavy and you want more practice than your text offers. - Precalculus (Stitz and Zeager) (Carl Stitz and Jeff Zeager)
A widely adopted open precalculus text with careful explanations, available as PDF and as interactive online lessons. Approved by the American Institute of Mathematics.
Start: Its function chapters explain why, not just how.
Calculus
I'm in MATH 140 or a later calculus course. Free textbooks with worked examples, lecture series, and problem books with answers.
- ★ CLP Calculus texts and problem books (Feldman, Rechnitzer, and Yeager, University of British Columbia)
Four free texts (differential, integral, multivariable, and vector calculus), each with a separate problem book that has hints, answers, and full solutions. The problem books are the best free source of calculus practice we know.
Start: CLP-1 problem book for derivatives; CLP-2 for integrals. - ★ [Used at Lawrence] Calculus, Volumes 1–3 (OpenStax, Rice University)
A conventional three-volume calculus sequence, similar in layout to commercial textbooks. Useful as a second explanation of any standard topic.
Start: Volume 1 covers limits, derivatives, and an introduction to integration. - ★ Paul's Online Notes: Calculus I, II, and III (Paul Dawkins, Lamar University)
Many students find these easier to read than their textbook: short explanations, lots of worked examples, and practice problems with step-by-step solutions for limits, derivatives, integrals, series, and multivariable calculus.
Start: Calculus I for MATH 140. Calculus II and III are linked from the site's menu. - Algebra, trig, and calculus cheat sheets (Paul Dawkins, Lamar University)
Printable reference sheets: algebra rules, common errors, trig identities, and derivative and integral tables. The "common algebra errors" sheet is useful before any exam.
Start: Print the algebra sheet for your notebook. - Active Calculus (Matt Boelkins and collaborators)
Built around short activities that ask you to work out ideas before they are stated. Good for understanding why derivatives and integrals work, not just the rules.
Start: Try the "preview activity" at the start of a section before reading it. - APEX Calculus (Gregory Hartman and collaborators)
A complete open calculus text with interactive 3D graphics in the online version. Approved by the American Institute of Mathematics. - MIT 18.01SC Single Variable Calculus (MIT OpenCourseWare)
A full self-study calculus course: lecture videos, short recitation videos by teaching assistants, problem sets, and exams with solutions.
Start: The recitation videos walk through one problem each and are good for a single stuck topic. - Essence of Calculus (3Blue1Brown) (Grant Sanderson)
A short animated series on the big ideas of calculus: derivatives as rates, integrals as accumulation, and why the two are connected. Best watched before or alongside a course, not instead of practice. - Professor Leonard lectures (Leonard (community college instructor), YouTube)
Full-length, unhurried classroom lectures on precalculus, calculus, and statistics. Long, but students who need every step written out like them.
Start: Search the channel for the exact topic rather than starting at lecture 1.
Proof, logic, and discrete math
I'm learning to write proofs or working with formal logic. Symbolic reasoning: proofs, sets, logic, counting, and graphs.
- ★ [Used at Lawrence] Discrete Structures (Kyle Ormsby and David Perkinson, Reed College)
The text used in Lawrence's discrete math course. Written for Reed's Math 113, it covers counting, sets, graph theory, probability, number theory and modular arithmetic, and generating functions.
Start: Reed's Math 113 course page (people.reed.edu/~davidp/113/) has lecture videos and review sheets that follow the book. - ★ Book of Proof (Richard Hammack)
A gentle, popular introduction to sets, logic, and proof techniques (direct, contrapositive, contradiction, induction). Many exercises have solutions.
Start: Part II, on how to write a proof, is the core. - forall x: Calgary (P. D. Magnus, Tim Button, and the Open Logic Project)
An open introduction to formal logic: truth tables, natural deduction, and first-order logic. Used in many philosophy and logic courses. - Discrete Mathematics: An Open Introduction (Oscar Levin)
Counting, sequences, logic and proofs, and graph theory, written for students meeting proofs for the first time. Approved by the American Institute of Mathematics.
Linear algebra and differential equations
I'm past calculus and into vectors, matrices, or ODEs. Free, well-regarded texts and video series for the second year of math.
- ★ Understanding Linear Algebra (David Austin, Grand Valley State University)
An open text that emphasizes geometric meaning and applications, with interactive computation built into the online version. - ★ Essence of Linear Algebra (3Blue1Brown) (Grant Sanderson)
Animated videos that show matrices as transformations of space. Many students say this is when linear algebra finally made sense. - MIT 18.06SC Linear Algebra (Gilbert Strang, MIT OpenCourseWare)
Strang's well-known lectures with recitation videos, problem sets, and exams with solutions. - Notes on Diffy Qs (Jiří Lebl)
A free introductory differential equations text covering first-order equations, linear systems, Fourier series, and Laplace transforms. Approved by the American Institute of Mathematics. - Paul's Online Notes: Differential Equations (Paul Dawkins, Lamar University)
Worked-example notes on first-order equations, second-order linear equations, Laplace transforms, systems, and series solutions, with practice problems.
Statistics and probability
I'm in a stats course or using statistics in psychology, biology, or economics. Open textbooks, visual explanations, and free apps for running analyses.
- ★ OpenIntro Statistics (Diez, Çetinkaya-Rundel, and Barr)
One of the most widely used free intro statistics texts, with real data sets, video overviews, and labs in R. Approved by the American Institute of Mathematics. - ★ Seeing Theory (Daniel Kunin, Brown University)
A visual introduction to probability and statistics in six interactive chapters, from basic probability through regression. Lets you watch the central limit theorem happen.
Start: Chapter 3, Probability Distributions. - Introduction to Modern Statistics (Mine Çetinkaya-Rundel and Johanna Hardin (OpenIntro))
A modern intro text that teaches inference through randomization and bootstrapping before formulas, with an emphasis on data and modeling. - Introductory Statistics 2e (OpenStax, Rice University)
A traditional one-term statistics text: descriptive statistics, probability, distributions, confidence intervals, and hypothesis tests. - Art of Stat web apps (Bernhard Klingenberg)
Free browser apps for exploring data, regression, distributions, sampling distributions, and inference, including bootstrap and permutation tests. Useful when you don't have statistical software. - StatQuest (Josh Starmer, YouTube)
Short, friendly videos that explain statistical and machine-learning ideas (p-values, regression, PCA) one picture at a time. - jamovi (The jamovi project)
Point-and-click statistics software, a free alternative to SPSS, built on R. Good for students who need t-tests, ANOVA, or regression without writing code.
Data, spreadsheets, and code
I need Excel, R, or Python for a class, a thesis, or a job. Free lessons and in-browser tools. No installation needed for most of these.
- ★ R for Data Science (2e) (Wickham, Çetinkaya-Rundel, and Grolemund)
The standard free introduction to doing data analysis in R with the tidyverse: importing, cleaning, visualizing, and summarizing data.
Start: The "Whole game" chapters get you to a working analysis fast. - ★ Python for Everybody (Charles Severance, University of Michigan)
A complete beginner's course in Python with a free textbook, video lectures, and auto-graded exercises. Assumes no programming background. - ★ Excel tutorials (GCFGlobal) (GCFGlobal / LearnFree)
Plain-language, step-by-step Excel lessons for complete beginners, with practice files. - Posit Cloud (Posit)
RStudio in a web browser, so you can run R without installing anything. - Google Colab (Google)
Python notebooks that run in the browser with common data libraries already installed. - Software Carpentry lessons (The Carpentries)
Short, tested lessons on the command line, version control with Git, and programming in Python or R, written for researchers. - Excel help and learning (Microsoft)
Microsoft's official tutorials and video training for Excel, from formulas and charts to PivotTables. Lawrence accounts include Microsoft 365.
Quantitative work in the sciences
The math in my physics, chemistry, or biology course is the problem. Units, equations, and models as they show up in science courses.
- ★ HyperPhysics (Carl R. Nave, Georgia State University)
A linked concept map of introductory physics with formulas, diagrams, and worked calculations. Quick for looking up how one idea connects to another. - ★ The Math You Need, When You Need It (SERC, Carleton College)
Short modules on the math that intro science courses assume: unit conversions, rearranging equations, slopes, logarithms, and density, each with practice problems.
Start: Start with unit conversions and rearranging equations. - PhET Interactive Simulations (University of Colorado Boulder)
Research-based simulations in physics, chemistry, and math (graphing lines, quadratics, fractions, vectors). Good for building intuition before solving problems. - University Physics, Volumes 1–3 (OpenStax, Rice University)
A calculus-based introductory physics text. Each chapter has worked examples with a "strategy, solution, significance" structure. - Chemistry 2e (OpenStax, Rice University)
A general chemistry text. Its appendices on essential math (exponents, logarithms, significant figures) are useful on their own. - Chemistry LibreTexts (LibreTexts)
A large library of open chemistry texts and modules, from general chemistry through physical chemistry. Search for a topic rather than browsing. - SI units (National Institute of Standards and Technology)
The official reference for SI base units, derived units, and prefixes.
Quantitative work in economics and social science
I need the math behind economics, or real data for a project. Open economics texts and reliable public data sources.
- ★ The Economy 2.0 (CORE Econ) (The CORE Team)
A free, data-driven introduction to economics developed by an international group of economists. Uses real data and models throughout. - ★ FRED economic data (Federal Reserve Bank of St. Louis)
Hundreds of thousands of economic time series (GDP, unemployment, inflation, interest rates) with instant graphs and downloads. - Principles of Economics 3e (OpenStax, Rice University)
A conventional principles text covering micro and macro. The appendix on using graphs in economics is a good refresher on slope and linear equations. - Our World in Data (Global Change Data Lab and University of Oxford)
Charts and downloadable data on health, population, energy, poverty, and more, each with its sources documented. Good for projects and for practicing reading graphs.
Graphing and computing tools
I want to graph something, check an answer, or explore an idea. Free calculators and math software. Check your course policy before using them on graded work.
- ★ Desmos graphing calculator (Desmos Studio)
A fast, easy graphing calculator in the browser. Add sliders to see how changing a coefficient changes a graph.
Start: Type y = a x^2 + b x + c and add sliders for a, b, and c. - GeoGebra (GeoGebra)
Graphing, geometry, 3D, and computer algebra in one free tool, with thousands of ready-made activities. - Wolfram|Alpha (Wolfram Research)
Answers math questions typed in plain language: solves equations, simplifies, differentiates, integrates, and plots. Best for checking your work after you've done it.
How to study math
I put in the hours but it isn't sticking, or math makes me anxious. Research-based study strategies and resources on math anxiety and mindset.
- ★ Six strategies for effective learning (The Learning Scientists)
Posters, slides, and bookmarks on six research-backed strategies: spaced practice, retrieval practice, elaboration, interleaving, concrete examples, and dual coding.
Start: Read the retrieval practice and interleaving posters first; they matter most for math. - Retrieval practice for students (Pooja K. Agarwal)
Short, research-based advice on studying by recalling and practicing instead of rereading. - youcubed (Stanford Graduate School of Education)
Resources on mathematical mindset and visual approaches to math. Helpful reading for students who believe they are "not a math person," and for the people who teach them.
Writing and presenting quantitative work
I have to write up math, make a chart, or present results. Typesetting, data visualization, and writing with numbers.
- ★ Learn LaTeX in 30 minutes (Overleaf)
The standard first tutorial for typesetting math with LaTeX in an online editor. The rest of Overleaf's documentation answers almost any later question. - Quantitative writing (SERC, Carleton College)
What it means to write with numbers, with tutorials and examples of quantitative writing assignments across disciplines. - Communication handouts, including data visualization (Carnegie Mellon University, Student Academic Success Center)
Printable handouts on scientific writing, presentations, research posters, tables and charts, and data visualization.
Beyond the course
I'm preparing for the GRE, or I want numbers to make sense in everyday life. Graduate admissions tests and quantitative reasoning for its own sake.
- ★ Official GRE prep materials (ETS)
Free official practice tests and a math review for the GRE quantitative section, from the test maker. - [Used at Lawrence] Contemporary Mathematics (OpenStax, Rice University)
A liberal-arts math text on sets, logic, probability, statistics, personal finance, and geometry. Good for quantitative reasoning outside a math major.
Start: The personal finance chapter covers interest, loans, and budgeting. - Math in Society (David Lippman)
Short chapters on voting, apportionment, finance, growth models, statistics, and graph theory as they come up in civic life.
Tutoring practice and training
I tutor (or want to) and want to get better at it. Standards and materials for peer tutors and the people who train them.
- ★ CRLA tutor training certification (ITTPC) (College Reading and Learning Association)
The standards the QRC trains to. Level 1 requires at least 10 hours of training on 8 topics and 25 hours of tutoring. Certification goes to programs, not individual tutors.
Start: Read the Level 1 topics list to see what your training covers. - QMaSC Handbook: training and mentoring chapters (Coulombe, O'Neill, and Schuckers, eds.)
Chapters 14 and 15 of this handbook collect training methods and practice scenarios written by directors of math and quantitative centers at peer colleges.
Start: Chapter 15, Practice and Mentoring, is a bank of tutoring scenarios.
Teaching quantitative reasoning
I teach a course with quantitative content, in any department. Free guides, activities, and open textbooks for faculty.
- ★ Developing quantitative reasoning (Nathan Grawe, SERC, Carleton College)
How to build quantitative reasoning into a course in any discipline: what QR is, principles for teaching it, designing assignments, and assessing them with rubrics. - ★ AIM approved open textbooks (American Institute of Mathematics)
A reviewed list of free math textbooks from precalculus through upper-division courses. Start here if you want to drop a commercial textbook. - MAA Instructional Practices Guide (Mathematical Association of America)
An evidence-based guide to classroom practices, assessment, and course design in college mathematics, with a companion book-study guide. - Teaching with Spreadsheets Across the Curriculum (SERC, Carleton College)
Ready-made modules in which students build Excel spreadsheets to answer questions in subjects from geology to economics.
Running a quantitative center
I support or plan quantitative learning at Lawrence. The professional literature on quantitative and math support centers.
- ★ QMaSC: A Handbook for Directors of Quantitative and Mathematics Support Centers (Coulombe, O'Neill, and Schuckers, eds. (2016))
The handbook for this field: management, outreach, faculty development, training, assessment, space design, and ten case studies of centers at colleges like Bates, Hamilton, Smith, and St. Lawrence.
Start: Chapters 9 (outreach) and 12 (virtual presence) shaped this directory. - Numeracy (journal) (National Numeracy Network)
The peer-reviewed, open-access journal on quantitative literacy across disciplines.