How to See an Equation
The art of algebraic reasoning
2026 · 160 pp
One hundred and fifty-six problems in classical algebra for the ambitious student, arranged by technique across two parts. Part one assembles the instruments, proof, number systems, identities, functions, inequalities, induction, and exponentials. Part two puts them to work, quadratics and polynomials, complex numbers, sequences, counting, the binomial theorem, the classical inequalities, and functional equations. Every problem is followed by a full discussion that names the central idea, gives the shortest honest proof, and marks the trap that catches the unwary.
A course in classical algebra for the reader who wants to do algebra, not merely read it. It is written for the ambitious student who has met the usual school syllabus and wants to meet what lies beyond: the Euclidean algorithm, Viète’s formulas, the factor theorem, Newton’s identities, the classical inequalities, and the rest of the inheritance.
The fifteen chapters fall into two parts. Foundations gathers the instruments, from proof and number systems through inequalities, induction, and exponentials. Algebra puts them to work, from quadratic and polynomial equations through complex numbers, sequences, counting, the binomial theorem, and functional equations. Each chapter requires only those before it, and every problem is chosen to reveal a distinct idea. The problems favour the concrete question over the abstract theorem, and each is worked in full, with the central technique named and the common trap marked.
Found an error? Let me know and I will correct it.