Learn · Practice · Integrate · Recognize
The Field Guide Series for Mathematics
The Field Guide Series for Mathematics is a coordinated collection of concise, visual resources designed to help readers learn mathematical structure, recognize the right ideas quickly, practice with purpose, and integrate methods across a topic.
Topics in the Field Guide Series ↓
A unified volume
Four coordinated formats for each topic
The four formats share notation, visual cues, and a common mathematical vocabulary while serving different study tasks. Each is designed to remain useful beside a textbook, notebook, or computer rather than replace a full course text.
- Learn
Field Guide
Essential ideas, maps, methods, examples, and connections.
- Practice
Field Workbook
Targeted calculation, investigation, explanation, and exploration.
- Integrate
Field Companion
Modules that connect theorems, recognition cues, and investigations.
- Recognize
Field Cards
Rapid identification, formulas, decision cues, and visual reference.
The Field Guide Series is available to students in 3 affordable formats:
eBook
$14.95
1-Color Comb-bound Paperback
$24.95
Full-Color Comb-bound Paperback
$34.95
The series
Topics in the Field Guide Series
01
Combinatorics
Designed as a compact companion to an undergraduate course in combinatorics, this Field Guide follows the enumerative spine from modeling and elementary counting through permutations, stars and bars, bijections, Catalan and Stirling families, inclusion-exclusion, symmetry, generating functions, recurrences, probability, partitions, graphs, posets, q-analogues, designs, codes, and matroids.
View the Combinatorics sampler (PDF) →02
Complex Analysis
Designed as a compact companion to an undergraduate course in complex analysis, this Field Guide follows the classical route from complex numbers, branches, and elementary functions through analyticity, Cauchy theory, power and Laurent series, residues, zero counting, conformal mapping, harmonic functions, and the Riemann sphere.
03
Div, Grad, Curl and the Integral Theorems
Vector calculus becomes easier to navigate when its operators and integral theorems are viewed as one local-to-global system. This unified volume brings together the Learn, Practice, Integrate, and Recognize modes for Div, Grad, Curl and the Integral Theorems. The mathematics flows from type and geometry to operators, potentials, orientation, line and surface integrals, Green's theorem, Stokes' theorem, the divergence theorem, and theorem selection.
04
Integration Techniques and Infinite Series
Calculus II becomes more manageable when the decision that comes before the calculation is made explicit. An integral may require a reverse chain rule, a reverse product rule, algebraic decomposition, a trigonometric identity, a symmetry argument, a numerical method, or a series expansion. An infinite series asks a parallel question: what structural pattern determines its behavior, and which convergence theorem actually applies?
05
Mathematical Statistics
Mathematical statistics becomes more manageable when the decision that comes before the calculation is made explicit. Begin with the model, parameter space, support, and source of randomness. Then follow the information through the statistic, its sampling distribution, the estimator or pivot, and the inferential statement.
06
Ordinary Differential Equations
Ordinary differential equations are often introduced as a sequence of techniques. Those techniques matter, but the more durable skill is structural recognition: identify the type of equation, decide what information is needed, and choose an analytical, geometric, numerical, transform, or series method that fits the question.
07
Probability
Designed as a compact companion to an undergraduate course in probability, this Field Guide records consistent parameterizations, summarizes principal formulas, and emphasizes relationships among families.
08
Probability Distributions
Probability distributions describe the possible values of a random variable and how probability is allocated among those values. They are fundamental objects in probability theory, but their usefulness goes beyond their formulas: a distribution is often identified by the mechanism that produces it. Repeated independent trials lead naturally to a binomial model, sampling without replacement to a hypergeometric model, and Poisson counts to exponential and gamma waiting times.
09
Real Analysis
Real analysis makes the foundations of calculus precise. This unified volume is designed as a working instrument: the Field Guide supplies the conceptual map; the Workbook turns definitions and theorem hypotheses into proof practice; the Companion connects local ideas into longer mathematical decisions; and the Field Cards provide a compact recognition system.
10
Vectors
Vectors are mathematical objects that move naturally among geometry, algebra, and application. This unified volume is designed as a working instrument: the Field Guide supplies the conceptual map; the Workbook turns definitions and methods into active practice; the Companion connects components, bases, products, curves, motion, and statics; and the Field Cards provide a compact recognition system.