The bibliography is a result of the thorough analysis of reviews on the books with the focus on the prevalence of similar opinions from diverse sources and the clarity of presentation as perceived after finishing the book.
The method of choosing a listed book is subjective, since there are examples of books frequently used and copiously advised to be used to teach high school students, but still furnishing a striving learner with the lower-quality content compared with their analogues.
Thus, the booklist below is a compilation of the resources developing the concept under discussion consistently and illustratively in the opinion of various readers,including the author.
1. Algebra by Israel M. Gelfand and Alexander Shen
2. Functions and Graphs by I. M. Gelfand, E. G. Glagoleva, E. E.Shnol
3. The Method of Coordinates by I. M. Gelfand, E. G. Glagoleva, A. A. Kirillov
The books with the lucid conceptual exposition apply familiar ideas to the seemingly complex areas of study. Have you ever read about the construction of the n-dimensional space in a book for the beginners? This is a certainly priceless opportunity to do so.
Recommended by:
Learners with different levels of mathematical knowledge and intuition would benefit from reading this piece of work. The authors demonstrate the development of mathematics starting with the basic laws of arithmetic. Thus, the book is, as stated by Albert Einstein, "a lucid representation of the fundamental concepts and methods of the whole field of mathematics".
The method of choosing a listed book is subjective, since there are examples of books frequently used and copiously advised to be used to teach high school students, but still furnishing a striving learner with the lower-quality content compared with their analogues.
Thus, the booklist below is a compilation of the resources developing the concept under discussion consistently and illustratively in the opinion of various readers,including the author.
1. Algebra by Israel M. Gelfand and Alexander Shen
2. Functions and Graphs by I. M. Gelfand, E. G. Glagoleva, E. E.Shnol
3. The Method of Coordinates by I. M. Gelfand, E. G. Glagoleva, A. A. Kirillov
The books with the lucid conceptual exposition apply familiar ideas to the seemingly complex areas of study. Have you ever read about the construction of the n-dimensional space in a book for the beginners? This is a certainly priceless opportunity to do so.
Recommended by:
- Chicago undergraduate mathematics bibliography
- Review of the books by the Department of Mathematics, Berkeley
- The first book is recommended by Art of Problem Solving administrators and members of the community
4. Principles of Mathematics by C. B. Allendoerfer, C. O. Oakley
A wonderful resource written more than half a century ago arranges and supplies a reader with other valuable references, including links to further reading on specific topics and articles from the mathematical journals accessible to the high-schoolers. Moreover, some used copies are ridiculously cheap on Amazon.
Recommended by:
5. What Is Mathematics? by Richard Courant and Herbert Robbins
Learners with different levels of mathematical knowledge and intuition would benefit from reading this piece of work. The authors demonstrate the development of mathematics starting with the basic laws of arithmetic. Thus, the book is, as stated by Albert Einstein, "a lucid representation of the fundamental concepts and methods of the whole field of mathematics".
Recommended by:
- Cambridge Mathematical Reading List
- TSR Recommended Mathematics Reading
- MAA Library Recommendations. The Basic Library List Committee considers this book essential for undergraduate mathematics libraries.
6. The Elements by Euclid
The classical treatise has been considered a benchmark of the geometry formalisation for over 1800 years till the beginning of the XX century. The list of axioms originally presented in the thirteen books was proven not to be exhaustive. Ergo, it is highly recommended to study the work of Euclid with a reading guide in order to grasp the material in its complete form. The editions by T.L.Heath provide commentaries shedding light on the corrections of the manuscript, while the full explanations and the further development of geometry are given in the book "Euclid and Beyond" by Robin Hartshorne. One of the first treatments of the foundations of geometry that still remains relevant is the published compilation of lectures by David Hilbert "Grundlagen der Geometrie".
Recommended by:
The classical treatise has been considered a benchmark of the geometry formalisation for over 1800 years till the beginning of the XX century. The list of axioms originally presented in the thirteen books was proven not to be exhaustive. Ergo, it is highly recommended to study the work of Euclid with a reading guide in order to grasp the material in its complete form. The editions by T.L.Heath provide commentaries shedding light on the corrections of the manuscript, while the full explanations and the further development of geometry are given in the book "Euclid and Beyond" by Robin Hartshorne. One of the first treatments of the foundations of geometry that still remains relevant is the published compilation of lectures by David Hilbert "Grundlagen der Geometrie".
Recommended by:
- Chicago undergraduate mathematics bibliography
- Albert Einstein referred to the work of Euclid as a "holy little geometry book". The Elements has influenced such scientists as Nicolaus Copernicus, Galileo Galilei, Johannes Kepler, and Sir Isaac Newton. Moreover, as Henry Ketcham writes in his book "The Life of Abraham Lincoln", Abe kept a copy of Euclid in his saddlebag, and studied it late at night by lamplight; he related that he said to himself, "You never can make a lawyer if you do not understand what demonstrate means; and I left my situation in Springfield, went home to my father's house, and stayed there till I could give any proposition in the six books of Euclid at sight".
