EulerPad

Math workbooks with worked solutions

Three printable workbooks, 250 problems each. Every problem has a step-by-step solution with the reason for each step, every chapter ends with the mistakes that cost the most marks, and every numerical answer is checked by computer before the book is built. Each comes with a free sample chapter.

250 problems · 25 chapters

Calculus I & II

250 problems on limits, derivatives, integrals, series and polar curves, with every step worked and the common mistakes named.

For students in Calculus I and II or AP® Calculus AB and BC, and the tutors and parents who help them. AP® is a trademark of the College Board, which does not endorse this book.

✓ Two PDFs: Problems (80 pages) and Worked Solutions (172 pages), US Letter, ready to print
✓ A worked solution for every problem, one step per line with the reason beside it
✓ An answer key per chapter, and the mistakes that cost the most marks on each topic
✓ 2 chapters (20 problems) written only for the workbook; the rest are revised from the free practice sets
Contents
  • Limits and continuity: Evaluating limits · Continuity and the intermediate value theorem★ · L'Hôpital's rule and indeterminate forms
  • Derivatives: Differentiation rules · Implicit differentiation · Derivatives of inverse functions and inverse trig functions · Related rates · Maxima and minima · The mean value theorem and Rolle's theorem · Newton's method for roots and minima
  • Integrals: Riemann sums · The fundamental theorem of calculus · Integration · Trigonometric substitution · Partial fractions and integrating rational functions · Improper integrals
  • Applications of integration: Area between curves · Volumes of revolution · Arc length and surface area of revolution
  • Sequences and series: Arithmetic and geometric sequences and sums · Series convergence tests · Ratio and root tests, and power series★ · Taylor series and linear approximation
  • Curves in the plane: Parametric and polar curves · Conic sections

★ Workbook-only chapter.

Buy the workbook · $15Free sample: Chapter 13 (PDF)
250 problems · 25 chapters

Probability & Statistics for Machine Learning

250 problems from counting and Bayes' rule to hypothesis tests, MLE, Markov chains and KL divergence, with every step worked.

For data scientists, ML engineers and students in a first probability or statistics course.

✓ Two PDFs: Problems (81 pages) and Worked Solutions (195 pages), US Letter, ready to print
✓ A worked solution for every problem, one step per line with the reason beside it
✓ An answer key per chapter, and the mistakes that cost the most marks on each topic
✓ 8 chapters (80 problems) written only for the workbook; the rest are revised from the free practice sets
Contents
  • Probability: Counting · Bayes' rule and conditional probability · Discrete random variables · The negative binomial, hypergeometric and multinomial distributions★ · Continuous random variables · Poisson processes and the exponential distribution★ · Joint, marginal and conditional densities★ · Transformations of random variables★ · Variance, covariance and correlation · Conditional expectation and the law of total variance · Moment generating functions★
  • The normal distribution and limits: The normal distribution and z-scores · The multivariate Gaussian · The law of large numbers, Markov's inequality and Chebyshev's inequality · Sampling distributions and the central limit theorem · Order statistics and Monte Carlo estimation★
  • Statistical inference: Maximum likelihood estimation · Hypothesis tests and p-values · Two-sample tests and A/B testing★ · Bootstrap and permutation tests★ · Chi-square tests · Simple linear regression · Bayesian inference
  • Processes and information: Markov chains · Entropy, cross-entropy and KL divergence

★ Workbook-only chapter.

Buy the workbook · $24Free sample: Chapter 24 (PDF)
250 problems · 25 chapters

Deep Learning Math by Hand

250 problems on gradients, backprop, attention, normalization and optimizers, worked out with pencil and paper.

For ML engineers preparing for interviews, students in a first deep learning course, and researchers who want to check a backward pass before trusting it.

✓ Two PDFs: Problems (78 pages) and Worked Solutions (219 pages), US Letter, ready to print
✓ A worked solution for every problem, one step per line with the reason beside it
✓ An answer key per chapter, and the mistakes that cost the most marks on each topic
✓ 7 chapters (70 problems) written only for the workbook; the rest are revised from the free practice sets
Contents
  • Foundations: Partial derivatives, gradients and Hessians · Matrix calculus conventions · Jacobians and the chain rule
  • Backprop by hand: Activation functions and their derivatives · The softmax Jacobian · Softmax cross-entropy, label smoothing and log-sum-exp★ · Regression gradients · Logistic regression · One-hidden-layer backprop, the whole backward pass
  • Minibatches and normalization: Batched backprop · Batch norm backward · Layer norm backward
  • Architectures: Residual connections and gradient flow★ · Convolution backward · Pooling, stride and padding backward★ · Backprop through time · Attention backward
  • Representation learning: Embeddings, weight tying and sparse gradients★ · Contrastive losses★
  • Training: Xavier and He initialization · Momentum, RMSProp and Adam · Regularization★ · Gradient clipping and learning-rate schedules★
  • Gradients of expectations: The ELBO and the reparameterization trick · Policy gradients and the log-derivative trick

★ Workbook-only chapter.

Buy the workbook · $29Free sample: Chapter 21 (PDF)

Questions

Isn't this on the site for free?

Partly, and we say so on each book. Most chapters started as free practice sets; the workbooks revise them for print, put them in course order, add an answer key and cross-references, and add 17 chapters that are not online at all.

What do I get?

Two PDFs per book, Problems and Worked Solutions, US Letter size, for printing or for a tablet. The problems volume leaves room to work under each problem.

I found a mistake.

Write to [email protected]. Corrected editions are free to everyone who bought the book.

Can I use it with a class?

Each copy is for one person. Teachers and tutors who want to use a book with a class can write to [email protected].