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This innovative textbook introduces a new pattern-based approach to learning proof methods in the mathematical sciences. Readers will discover techniques that will enable them to learn new proofs across different areas of pure mathematics with ease. The patterns in proofs from diverse fields such as algebra, analysis, topology and number theory are explored. Specific topics examined include game theory, combinatorics, and Euclidean geometry, enabling a broad familiarity. The author, an experienced lecturer and researcher renowned for his innovative view and intuitive style, illuminates a wide range of techniques and examples from duplicating the cube to triangulating polygons to the infinitude of primes to the fundamental theorem of algebra. Intended as a companion for undergraduate students, this text is an essential addition to every aspiring mathematician’s toolkit.

Mathematics. --- Number Theory. --- Geometry. --- Combinatorics. --- Analysis. --- Topology. --- Mathematics Education. --- Global analysis (Mathematics). --- Number theory. --- Mathématiques --- Analyse globale (Mathématiques) --- Géométrie --- Théorie des nombres --- Topologie --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Mathematical analysis. --- Analysis (Mathematics). --- Study and teaching. --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Combinatorics --- Mathematical analysis --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Number study --- Numbers, Theory of --- Euclid's Elements --- Math --- Science --- Combinatorial analysis. --- Mathematics—Study and teaching . --- 517.1 Mathematical analysis