@article{1439920,
      recid = {1439920},
      author = {Tóth, Gábor,},
      title = {Elements of mathematics : a problem-centered approach to  history and foundations /},
      pages = {1 online resource :},
      abstract = {This textbook offers a rigorous presentation of  mathematics before the advent of calculus. Fundamental  concepts in algebra, geometry, and number theory are  developed from the foundations of set theory along an  elementary, inquiry-driven path. Thought-provoking examples  and challenging problems inspired by mathematical contests  motivate the theory, while frequent historical asides  reveal the story of how the ideas were originally  developed. Beginning with a thorough treatment of the  natural numbers via Peano's axioms, the opening chapters  focus on establishing the natural, integral, rational, and  real number systems. Plane geometry is introduced via  Birkhoff's axioms of metric geometry, and chapters on  polynomials traverse arithmetical operations, roots, and  factoring multivariate expressions. An elementary  classification of conics is given, followed by an in-depth  study of rational expressions. Exponential, logarithmic,  and trigonometric functions complete the picture, driven by  inequalities that compare them with polynomial and rational  functions. Axioms and limits underpin the treatment  throughout, offering not only powerful tools, but insights  into non-trivial connections between topics. Elements of  Mathematics is ideal for students seeking a deep and  engaging mathematical challenge based on elementary tools.  Whether enhancing the early undergraduate curriculum for  high achievers, or constructing a reflective senior  capstone, instructors will find ample material for  enquiring mathematics majors. No formal prerequisites are  assumed beyond high school algebra, making the book ideal  for mathematics circles and competition preparation.  Readers who are more advanced in their mathematical studies  will appreciate the interleaving of ideas and illuminating  historical details.},
      url = {http://library.usi.edu/record/1439920},
      doi = {https://doi.org/10.1007/978-3-030-75051-0},
}