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- 03_mathematical_logic_and_foundations:
- lectures:
- Montalban, A. 2020. Math 125A Mathematical Logic
- readings:
- Hinman, P.G. 2005. Fundamentals of Mathematical Logic
- Kunen, K. 2007. The Foundations of Mathematics
- Magnus, P.D., Button T., Trueman R., Zach T. 2023. forallx An Introduction to Formal Logic. Calgary
- Rautenberg, W. 2009. A Concise Introduction to Mathematical Logic. 3rd Edition
- The Open Logic Project. 2016. Sets, Logic, Computation
- Ben-David, S. 2015. University of Waterloo CS 245 Logic and Computation
- assignments:
- exams:
- 03_mathematical_logic_and_foundations/03Exx_set_theory:
- lectures:
- Montalban, A. 2020. U.C. Berkeley Math 135 Intro to Set Theory
- current: 2. Set Theory. Basic concepts
- readings:
- Hammack, R. 2018. Book of Proof. 3.3 ed. Richmond, Virginia
- Chapter 1: Sets
- assignments:
- exams:
- 15_linear_and_multilinear_algebra;matrix_theory:
- lectures:
- Censor, A. 2015. Technion International School of Engineering Algebra 1M International Course No. 104016
- current: Lecture 05 - Complex numbers: *
- Strang, G. 2005. MIT 18.06 Linear Algebra:
- current:
- Strang, G. 2020. A 2020 Vision of Linear Algebra.
- Khan Academy. Linear algebra
- Edx: GTx: Explore the fundamentals of linear algebra
- readings:
- https://04.phf-site.com/2017/02/algebra-2015-by-aviv-censor-at-technion.html
- what is mathematics?. richard courant.pdf : chapter iii, iv, v
- https://ocw.mit.edu/courses/18-06sc-linear-algebra-fall-2011/
- recitations:
- assignments:
- exams:
- 26_real_functions:
- lectures:
- calculus:
- Censor, A. 2013. Technion International School of Engineering Differential and integral Calculus 1 Course no. 104003
- current: Calculus - 01: *
- Jerison, D. 2006. MIT 18.01 Single Variable Calculus
- current: Lecture 01 ｜ MIT 18.01 Single Variable Calculus, Fall 2007 [7K1sB05pE0A]: *
- Hammack, R. 2020. Hammack's Calculus I
- current: Hammack's Calculus I, Lecture 1
- https://www.khanacademy.org/math/calculus-1
- https://ocw.mit.edu/courses/18-014-calculus-with-theory-fall-2010/
- Censor, A. 2015. Technion International School of Engineering Differential and integral Calculus 2 Course no. 104004:
- current: None
- https://04.phf-site.com/2017/02/differential-and-integral-calculus-2-by.html
- analysis:
- Casey Rodriguez. 2020. MIT 18.100A Real Analysis
- Hardy G.H. 2021. A Course in Pure Mathematics. The Project Gutenberg.pdf
- readings:
- https://ocw.mit.edu/courses/18-01-single-variable-calculus-fall-2006/
- Courant, R., Robbins, H. 1996. What is Mathematics. Oxford University Press
- chapter vi, viii
- recitations:
- assignments:
- exams:
============================================================================================================
next₁:
- 00_general_and_overarching_topics;collections:
- lectures:
- Wildberger, N.J. 2009. Insights into Mathematics Math Foundations
- current: 2 Arithmetic with numbers ｜ Arithmetic and Geometry Math Foundations 2 ｜ N J Wildberger : *
- basics:
from: 1 What is a number？ ｜ Arithmetic and Geometry Math Foundations 1 ｜ N J Wildberger
to: 17 Extremely big numbers ｜ Arithmetic and Geometry Math Foundations 17 ｜ N J Wildberger
- others:
66 Decimal numbers ｜ Arithmetic and Geometry Math Foundations 66 ｜ N J Wildberger
81 Measurement, approximation and interval arithmetic (I) ｜ Real numbers and limits Math Foundations 81
82 Measurement, approximation + interval arithmetic (II) ｜ Real numbers and limits Math Foundations 82
89 Fractions and repeating decimals ｜ Real numbers and limits Math Foundations 89 ｜ N J Wildberger
93 The magic and mystery of ＂pi＂ ｜ Real numbers and limits Math Foundations 93 ｜ N J Wildberger
104 Rational number arithmetic with infinity and more ｜ Real numbers and limits Math Foundations 104
210 Numbers as multipliers + particle⧸antiparticle duality I ｜ Data Structures Math Foundations 210
211 Numbers as multipliers + particle⧸antiparticle duality II ｜ Data Structures Math Foundations 211
- more on real number:
from: 111 Real numbers and Cauchy sequences of rationals(I) ｜ Real numbers and limits Math Foundations 111
to: 116 Difficulties with Dedekind cuts ｜ Real numbers and limits Math Foundations 116 ｜ N J Wildberger
- more on natural numbers:
from: 155 The realm of natural numbers ｜ Data structures in Mathematics Math Foundations 155
to: 157 The algebra of natural number multisets ｜ Data structures in Mathematics Math Foundation 157
- readings:
- Kent State Department of Mathematical Sciences. 2008. Fundamentals of Mathematics I
- current position: pg. 22: example 3
- Kent State Department of Mathematical Sciences. 2008. Fundamentals of Mathematics II
- current position: not started
- Kent State Department of Mathematical Sciences. 2008. Fundamentals of Mathematics III
- current position: not started
- Kent State Department of Mathematical Sciences. 2008. Fundamentals of Mathematics IV
- current position: not started
- Kent State Department of Mathematical Sciences. 2008. Fundamentals of Mathematics V
- current position: not started
- https://www.khanacademy.org/math/k-8-grades
- current position: 3rd grade
- recitations:
- assignments:
- exams:
- 03_mathematical_logic_and_foundations/03Fxx_proof_theory_and_constructive_mathematics:
- lectures:
- readings:
- Hammack, R. 2018. Book of Proof. 3.3 ed. Richmond, Virginia
- Aigner, M. Günter, M.Z. 2010. Proofs from The Book. 4 ed. Springer
- Radcliffe, M. Carnegie Mellon University Math 127 Logic and Proof Logic and Proof
- Velleman, D.J. 2019. How to Prove It A Structured Approach
- Dunham, W. 1990. Journey Through Genius The Great Theorems Of Mathematics
- assignments:
- exams:
- 12_field_theory_and_polynomials:
- lectures:
- readings:
- recitations:
- assignments:
- exams:
- 20_group_theory_and_generalizations:
- lectures:
- readings:
- recitations:
- assignments:
- exams:
============================================================================================================
next₂:
- 51_geometry
- lectures:
- Geometry: https://www.khanacademy.org/math/geometry-home
- current:
- High school geometry: https://www.khanacademy.org/math/geometry
- readings:
- Geometry - Euclid and Beyond. 2000. Robin Hartshorne
- Euclid's Elements Book I - VI. 2007. John Casey. Euclid
- Geometry. 2000. C. Jurgensen. G. Brown. W. Jurgensen
- what is mathematics?. richard courant.pdf : chapter iii, iv, v
page 142 in pdf. page 117 in text.
- recitations:
- assignments:
- exams:
- 00_general_and_overarching_topics; collections/00A71_general_theory_of_mathematical_modeling:
- lectures:
- Mathematical Modeling : Analysis and Applications
- Edx: DelftX: MathMod1x: Modelling with Differential Equations
- Edx: GeorgetownX: PHYS-155 : Mathematical and Computational Methods:
- Coursera: Precalculus through Data and Modelling Specialization
- readings:
- https://ocw.mit.edu/courses/18-311-principles-of-applied-mathematics-spring-2014/
- assignments:
- exams:
- 54_general_topology
- lectures:
- readings:
- Munkres, J.R. 2000. Topology. 2nd Edition
- recitations:
- assignments:
- exams:
============================================================================================================
next₃:
- 01_History_and_biography
- lectures:
- Wildberger, N.J. 2012. Insights into Mathematics Math History
- current: 1a Pythagoras' theorem (a) ｜ Math History ｜ NJ Wildberger : *
- readings:
- what is mathematics?. richard courant.pdf
- current position: not started
- recitations:
- assignments:
- exams:
============================================================================================================
- next field template:
- lectures:
- readings:
- assignments:
- exams:
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