Parabolic Problems

David Angell studied mathematics at Monash University and the University of New South Wales, Australia, earning a Ph.D. from the latter institution with a thesis on Mahler’s method in transcendence theory. He has been a member of the academic staff in the School of Mathematics at UNSW since 1989, and has consistently received glowing evaluations of his teaching both from colleagues and from students. David has taught a wide variety of mathematics subjects, but his favourites have always been number theory and discrete mathematics. He is particularly interested in teaching students to produce proofs and other mathematical writing which are clearly expressed, logically impeccable and engaging for the reader. David is strongly committed to extension activities for secondary school students. He has for many years been the problems editor for Parabola, the online mathematics magazine produced by UNSW, as well as contributing a number of articles to the magazine. He has also given talks on a wide variety of topics to final-year secondary students. His text Irrationality and Transcendence in Number Theory was published by CRC Press, Taylor & Francis in 2022.Beyond mathematics, David is an enthusiast for wilderness activities and has undertaken expeditions in Australia, Greenland, Nepal, Morocco and many other areas. He is a keen amateur musician, and is the founding conductor of the Bourbaki Ensemble, a chamber string orchestra based in Sydney, Australia.Thomas Britz studied mathematics and physics at Aarhus University, M.I.T. and Queen Mary University of London. After receiving a Ph.D. in mathematics from Aarhus University, Thomas completed postdoctoral fellowships at Victoria University, BC, the Technical University of Denmark and the University of New South Wales. Thomas has been a member of the School of Mathematics and Statistics at UNSW Sydney since 2010 and is currently the president of the Combinatorial Mathematics Society of Australasia (CMSA).In addition to his research on combinatorics and its applications, Thomas spends great effort to support and care for students and their education, and he strongly promotes the use of caring and emotions in education among fellow teachers. As chief editor of Parabola since 2014, Thomas has invited readers and contributors from all around the world to enjoy and create its mathematical content, so that it is now the largest international maths journal for students and anyone else interested in maths. Thomas is also a father, and he enjoys a busy life with his awesome partner and lovely children. He loves to solve puzzles and think about things, often more than is good for him.

"Happy 60th birthday Parabola! If you are in maths education, you will find it a unique and remarkable magazine, a treasure trove of interesting material and brilliant problems, more than 300 of which are in Parabolic Problems."-Alex Bellos, The Guardian"This is a stunningly good book! [...] [W]ith an appropriate class, these would add a good degree of challenge and encourage students to think a little more widely about applying their mathematical knowledge to unfamiliar areas."-Peter Hall, The Mathematical Gazette

• 1. Problems. 2. Solutions. 3. Some Useful Problem-solving Techniques. 3.1. Greatest Common Divisor. 3.2. Solving Linear Diophantine Equations. 3.3. Modular Arithmetic. 3.4. Graph Theory. 3.5. Basic Combinatorics. 3.6. The Binomial Theorem. 3.7. Some Trigonometric Formulae. 3.8. Proof by Mathematical Induction. 3.9. Pick’s Theorem. 3.10. Roots and Coefficients of Polynomials. 3.11. Inequalities.