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Mathematics and mathematics education research have an ongoing interest in improving our understanding of mathematical problem posing and solving. This book focuses on problem posing in a context of mathematical giftedness. The contributions particularly address where such problems come from, what properties they should have, and which differences between school mathematics and more complex kinds of mathematics exist. These perspectives are examined internationally, allowing for cross-national insights. The Editors Deniz Sarikaya is a guest researcher at the University of Copenhagen and the Technical University of Denmark (funded by the DAAD) and postdoctoral researcher at the Vrije Universiteit Brussel (within an FWO-project). Lukas Baumanns did his doctorate on problem posing at the University of Cologne. Currently he works at the Chair of Special Education in Mathematics and focuses on early mathematics learning and mathematical difficulties. Karl Heuer is an assistant professor in Discrete Mathematics at the Technical University of Denmark. He mainly works in Graph Theory, but is also active in enrichment programmes. He obtained his PhD in mathematics at the University of Hamburg. Benjamin Rott is a professor of Mathematics Education at the University of Cologne. He obtained a PhD at the University of Hannover, worked at the University of Education Freiburg and the University of Duisburg-Essen. His research interests include problem posing/solving, giftedness, and beliefs. .

Mathematics. --- General Mathematics and Education. --- General Mathematics. --- Mathematics --- Study and teaching.

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Dieses Open-Access-Buch beschreibt die theoriebasierte Entwicklung einer semesterbegleitenden Maßnahme zur Förderung der Problemlösekompetenz von Studienanfänger:innen der Fachmathematik und des gymnasialen Lehramts, sowie die zyklische Modifikation dieser Maßnahme im Sinne der Entwicklungsforschung. Begleitend dazu wurden, mit dem Ziel, grundlegende Erkenntnisse zum studentischen Problemlösen zu gewinnen, systematische Beobachtungen von Bearbeitungsprozessen zu typischen Übungsaufgaben durchgeführt. Hierbei hat sich insbesondere die Rolle des Vorwissens als entscheidender Faktor herausgestellt. Der Autor Thomas Stenzel arbeitet in der Mathematikdidaktik an der Universität Duisburg-Essen. Promoviert hat er 2021 bei Prof. Dr. Andreas Büchter. Sein Forschungsschwerpunkt liegt in der Hochschuldidaktik sowie im Bereich des Problemlösens.

Mathematics. --- General Mathematics and Education. --- Aufgabenbasierte Interviews --- Quantitative Forschung --- Problemlösekompetenz --- Studienanfänger --- Problemlösen --- Bearbeitungsprozesse --- Übungsaufgaben

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This textbook focuses on the basics and complex themes of group theory taught to senior undergraduate mathematics students across universities. The contents focus on the properties of groups, subgroups, cyclic groups, permutation groups, cosets and Lagrange’s theorem, normal subgroups and factor groups, group homomorphisms and isomorphisms, automorphisms, direct products, group actions and Sylow theorems. Pedagogical elements such as end of chapter exercises and solved problems are included to help understand abstract notions. Intermediate lemmas are also carefully designed so that they not only serve the theorems but are also valuable independently. The book is a useful reference to undergraduate and graduate students besides academics.

Mathematics. --- Algebra. --- Cryptography. --- Data encryption (Computer science). --- Engineering mathematics. --- General Mathematics and Education. --- Cryptology. --- Engineering Mathematics. --- Teoria de grups

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This book contains a large variety of intriguing puzzles with detailed ingenious solutions generally not found elsewhere. This book is a great treasure for everybody who enjoys the beauty of fascinating world of recreational mathematics. Puzzles in the book can be browsed at random as these are not grouped in any orderly manner. Apart from puzzle enthusiasts and mathlovers, the book is considered of immense value for aspirants of Math Olympiad, CAT/MBA and job interviews of big companies like Google, Microsoft, Amazon, Apple, Facebook, Yahoo, NVidia, Oracle, Adobe, Morgan Stanley, Bloomberg, etc. The title of puzzles has been suitably framed. Repetition of similar type of puzzles has been avoided to keep the book in a concise form. However, important aspects of similar puzzles, if any, have been covered in comments section. This book is divided into four chapters (Chaps. 1–4): Chapter 1 contains 25 short riddles and brainteasers. These puzzles vary from simple but tricky to challenging ones. Chapter 2 contains detailed solutions to all the short riddles and brainteasers given in Chapter 1. Chapter 3 contains 125 creative puzzles of varying difficulty level covering arithmetic and algebraic puzzles on clock, calendar, weight, age and digital puzzles, geometric puzzles, logical reasoning puzzles, and combinatorial puzzles, match puzzles and game puzzles like “kaun banega crorepati” (who will become a Decamillionaire), new year winner, winning numbers, etc. Some famous and old puzzles like Cheryl’s birthday, Bachets weight, liquid decanting, crossing bridge/river/desert, etc., have also been included so that readers can find all types of puzzles at one place. Only basic mathematics is required to solve these puzzles, but most of these puzzles are tricky and can be simplified by ingenious ideas. Chapter 4 contains detailed solutions to all the creative puzzles given in Chapter 3.

Mathematics. --- Mathematics in Popular Science. --- General Mathematics and Education. --- Applications of Mathematics. --- Math --- Science --- Mathematical recreations. --- Mathematical puzzles --- Number games --- Recreational mathematics --- Recreations, Mathematical --- Puzzles --- Scientific recreations --- Games in mathematics education --- Magic squares --- Magic tricks in mathematics education

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This volume is an original collection of articles by 44 leading mathematicians on the theme of the future of the discipline. The contributions range from musings on the future of specific fields, to analyses of the history of the discipline, to discussions of open problems and conjectures, including first solutions of unresolved problems. Interestingly, the topics do not cover all of mathematics, but only those deemed most worthy to reflect on for future generations. These topics encompass the most active parts of pure and applied mathematics, including algebraic geometry, probability, logic, optimization, finance, topology, partial differential equations, category theory, number theory, differential geometry, dynamical systems, artificial intelligence, theory of groups, mathematical physics and statistics.

Mathematics. --- Algebraic geometry. --- Probabilities. --- History. --- Algebraic topology. --- Differential equations. --- General Mathematics and Education. --- Algebraic Geometry. --- Probability Theory. --- History of Mathematical Sciences. --- Algebraic Topology. --- Differential Equations. --- 517.91 Differential equations --- Differential equations --- Topology --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Algebraic geometry --- Geometry --- Math --- Science --- Matemàtica