Math books

How to Solve It (1945) is a small volume by mathematician George Pólya describing methods of problem solving.

How to Solve It suggests the following steps when solving a mathematical problem:

  1. First, you have to understand the problem.
  2. After understanding, then make a plan.
  3. Carry out the plan.
  4. Look back on your work. How could it be better?

If this technique fails, Pólya advises: “If you can’t solve a problem, then there is an easier problem you can solve: find it.” Or: “If you cannot solve the proposed problem, try to solve first some related problem. Could you imagine a more accessible related problem?”

Problem-Solving Methods in Combinatorics – An Approach to Olympiad Problems, Pablo Soberón

Vector and Linear Algebra by Professor Risto Malcevski, Skopje, 2007
Content: Determinants of the second and third row, vector algebra, analytical geometry in space, linear algebra.

Introduction of discrete and continuous random variable – Zoran Trifunov, Elena Karamazova, Tatjana Atanasova-Pachemska. LAP Lambert Academic Publishing (2015-11-03)
Content: Introduction and solved examples with visualization of discrete and continuous random variables.

Mathematics – Tatjana A. Pacemska, Limonka Lazarova. This is a textbook with included examples, for the students in higher classes of secondary school. The content are topics from calculus.

Zanichelli is an Italian publishing house that publishes textbooks for schools. It has also a site rich of online resources , especially for high school: exercises, classes, interactive tests, problems and realities.

Here we find the math ebooks that a teacher has written for classes of a high school.


Problem Solving Strategies by Arthur Engel

The book “Problem Solving Strategies” by Arthur Engel, editors SPRINGER, was written as an aid for the preparation of the German teams that were to participate in the IMO competition. With this goal in view, it is a demanding book but clearly it is still very useful for developing problem solving skills. As it is specified in the preface to the book it aims at any individual that is interested in solving tough and interesting problems based on school mathematics.

The book presents various strategies and for each of them it starts with typical examples illustrating the main ideas involved. Then it goes on to present many problems and explain their solutions.

It can be used in a regular mathematics class at the upper secondary cycle of a school as a supplement to the work related to the ordinary syllabus for purposes of enriching the learning process and for identifying the value of doing mathematics.

  • The book obviously concentrates on tough approaches and examples thus making it difficult for the average teacher and student
  • This book is a challenge for anyone that wants to enrich his/ hers mathematical skills and particularly the problem skills.
    It is a source for those interested in participating in mathematics competitions.

It contains various notes on special topics of mathematics suitable for mathematical competitions.

Problems in elementary mathematics for home study, by N. ANTONOV, M. VYGODSKY, V. NIKITIN, A> SANKIN. Translated from the Russian by Leonid Levant. MIR PUBLISHERS, MOSCOW 1974

Problems in elementary Mathematics  by V. LIDSKY, L. OVSYANNIKOV, A. TULAIKOV, M. SHABUNIN. Translated from the Russian by V. VOLOSOV, MIR PUBLISHERS, MOSCOW 1973

Heron, J. ( 1999 ) The complete facilitator’s handbook.London:Kogan Page.

Tough, A. (1979 ) The adult’s  learning  project’s. Toronto: Ontario Institute  for students in Education.

JohanesLehman ( 1980 ) Kurzweil durchMathe. Leipzig :Urania – Verlag.

Сергеева Т. Ф., Пронина Н. А.,Сечкарева Е. В. (2011 ) Система работiъ с одареннiъми детъми: теория и практика




Autumn mathematical tournament “Crnorizec Hrabar” in mathematics and computer science

Real-World Problems for Secondary School Mathematics Students. Solving real world problems often leads to a typical decision situation where you (we hope together with your students) will ask: Should we stop working on our
problem now? Do we have enough information to solve the real world problem? These are not typical questions asked in mathematics lessons. What students should learn when they solve real world problems is that an exact calculation is not enough for a good solution. They should learn the whole process of modelling from the first step abstracting important information from the complex real world situation, to the next steps of the mathematical modelling process.

This packet contains open-ended questions for grades 4, 5, and 8 as well as openresponse questions for Algebra I / Probability / Statistics and Geometry. The high school questions were developed as part of professional development provided to mathematics teachers on how to adapt textbook or other problem sources into openended questions. As presently configured, many of these questions can be used in classrooms for assessment purposes. However, the teacher should consider modifying the problems to provide additional practice to their students on how to answer openended questions.

Effects of the application of information – computer technology in teaching mathematics.

The purpose of this master thesis is to determine the effects of application of ICT in teaching mathematics. The thesis presents the results of surveys made by students about their thinking, attitudes and acceptability of instruction in applied ICT. An analysis of the results of an interview done by teachers of primary education for their readiness, education on the use of ICT in teaching and their views on educational software. The publication as a topics contains: Information Technology in Teaching Mathematics, geogebra mathematics educational software and Research Methodology.

The impact of the use of educational software in mathematics in primary education aimed at improving the work with gifted students.
Learning improves through usage of modern methods and techniques of work and that in other words is computer technology and educational software. Following the activities of students and recieving feedback is of the out most importance to strenghten the gained knowlege and the effect of the education. Especially for mathematics as a science, if in early age the students overcome the problems more efficienty, then they will be more successfull in upper classes. Also by implementing software in mathematics class the students are given bigger motivation and interest. The SMART table and the usage of the SMART Notebook software has attracted the attention of both students and their parents.

Mathematical texts for gifted students – high school) autor Risto Malcheski

Crux Mathematicorum is an internationally respected source of unique and challenging mathematical problems published by the CMS. Designed primarily for the secondary and undergraduate levels, and also containing some pre-secondary material, it has been referred to as “the best problem solving journal in the world”. All the problems and solutions are fully peer-reviewed for clarity, completeness and rigour by academic and professional mathematicians. Crux includes an “Olympiad Corner” which is particularly helpful for students preparing for math competitions.

Mathematics Magazine offers lively, readable, and appealing exposition on a wide range of mathematical topics.

The American Mathematical Monthly publishes articles, notes, and other features about mathematics and the profession. Its readers span a broad spectrum of mathematical interests and abilities. Authors are invited to submit articles and notes that bring interesting mathematical ideas to a wide audience of Monthly readers.

The College Mathematics Journal is designed to enhance classroom learning and stimulate thinking regarding undergraduate mathematics. It publishes articles, short Classroom Capsules, problems, solutions, media reviews, and other pieces. All are aimed at the college mathematics curriculum with emphasis on topics taught in the first two years.

TALIS – Publikations  (An International Perspective on Teaching and Learning)