Preface - What is Suran?

PART 1.
Prehistoric times

Numbers / 1 / 2 / Numerals / Natural numbers / 0 / Four basic operations / Multiplication tables / Babylonian mathematics / Positive numbers / Negative numbers / Even and odd numbers / Multiples and divisors / Sequences / Units / Decimal system / Binary system / Points / Straight lines / Planes / Space / Area / Volume / Concentration and density / Triangles / Pythagorean theorem / Pythagorean numbers / Angles / Rectangles / Polygons / Circles / Pi / Polyhedrons / Column I - What mathematics cannot do

PART 2.
youth of the world

Square root / nth power / nth root / magic square / abacus / mental calculation / infinity / prime numbers / prime factorization / ratio / golden ratio / silver ratio / bronze ratio / rounding / factorial / literal expression / coefficient / binomial theorem / Pascal's triangle / equality / inequality / equation / solution / linear equation / simultaneous equations / quadratic equation / factorization / cubic equation / algebra / geometry / Euclidean geometry / parallel / perpendicular / alternate angles / congruence / similarity / line segment bisector / angle bisector / midpoint connection theorem / Cheba's theorem / proof / syllogism / excluded middle / contraposition / Barry's method / mathematical induction / universal proposition / trigonometric ratios / trigonometric functions / Column II - Meaning of construction

PART 3.
Middle Ages and Early Modern Period

Law of sines and cosines / Fibonacci sequence / Mathematical arithmetic / Mean / Percentage / Fraction / Decimal numbers / Finite decimals and recurring decimals / Real numbers / Rational numbers and irrational numbers / Proportionality / Inverse proportion / Function / Inverse function / Linear function / Quadratic function / Intercept / Ellipse / Parabola / Conic section / Differentiation / Differential equation / Integration / Trapezoidal formula / Fundamental theorem of calculus / Analysis / Limit / Rolle's theorem / Logarithm / Napier number / Cartesian coordinates / Cartesian geometry / Graph / Vertical line / Polar coordinates / Vector / Matrix / Imaginary number / Complex number / De Moivre's theorem / Euler's formula / Radial method / Exponential function / Logarithmic function / Number theory / Mersenne number / Euler's theorem / Remainder theorem / Modular operation / Cryptography / Column III - Pure and applied mathematics

PART 4.
late modern times

Mathematician / Set / Venn diagram / Infinite set / Empty set / Continuum hypothesis / Ordinal numbers and cardinal numbers / Peano axioms / Commutative law / Associative law / Curve / Non-Euclidean geometry / Elliptic geometry / Hyperbolic geometry / Riemannian geometry / Dimension / Coefficient / Infinite series / Taylor expansion / Newton's method / Oscillation / Convergence and divergence / Gaussian plane / Complex function / Complex analysis / Fourier series expansion / Laplace transform / Gamma function / Partial differentiation / Probability / Theoretical value / Significant figures / Statistics / Variance / Covariance / Regression analysis / Sample survey / Googol / Hyperreal number / Maximum and minimum / Fixed point theorem / Chaos theory / Game theory / Topology / Möbius strip / Four-color problem / Schrödinger equation / Fractal / Hilbert space / Linear algebra / Vector space / Abstract algebra / Column IV - The period of establishment of mathematics and the number of search results

PART 5.
hyundai

Groups / Rings and fields / Permutations / Combinations / Repunit numbers / Calculators / Computers / Algorithms / Truth values ​​/ NAND / Fuzzy logic / Game of Life / Random numbers / Entropy / Mathematics of origami / Knot theory / Foundations of mathematics / Gödel's incompleteness theorem / Diagonal argument / Hilbert's Hotel / Pseudo-infinite and practical / Axiom of choice / Paradoxes / Epimenides' paradox / Self-reference paradox / Banach-Tarski theorem / Network theory / Erdős number / Category theory / Bayesian inference / Black-Scholes equation / Traveler's problem / Workload problem / Monty Hall problem / RSA cryptography / Fermat's Last Theorem / Poincaré conjecture / Collatz conjecture / Riemann hypothesis

Conclusion - The Future of Mathematics

index
References

of the concept, by the concept, for the concept
A single visual dictionary of math concepts

There is no one who does not know the importance of the concept.
However, it is not easy to understand the concept explanations in textbooks after reading them once or twice.
It is introduced briefly in just a few lines, and the expressions are stiff, making it difficult to remember.
At this time, not many students delve into the concept.
Most people start solving problems with a vague understanding, but then get stuck and go back to explaining the concepts.
And you lose confidence in math.
"Dictionary of Mathematical Concepts: Understanding with Pictures, Without Memorization" explains math concepts in a conversational manner so that anyone can follow along.
By combining pictures that intuitively express abstract concepts, we have made it possible to imprint mathematical concepts just by looking at them.
Unlike workbooks or math books that make your head spin the moment you open them, you can look at them without any burden, and the concepts stick without you having to try hard to memorize them.


If you just follow the concept of the tail chasing its own tail
Math is visible, scores go up

All concepts in mathematics are interconnected.
Calculus learned in high school cannot be separated from functions learned in middle school, and prime numbers (natural numbers greater than 1 that have only 1 and themselves as divisors) learned in middle school cannot be separated from divisors learned in elementary school.
Reflecting this property of mathematics, the book provides a list of other concepts connected to the concept and the page number of each concept at the end of each explanation.
For example, the concept of connection between prime numbers (p. 78) is presented as infinity (p. 77), prime factorization (p. 79), number theory (p. 197), Mersenne numbers (p. 198), RSA cryptography (p. 327), and the Riemann hypothesis (p. 331).
There is no need to stress yourself out and force yourself to memorize math concepts.
You just have to follow the 'tail chasing its own tail' concept.


From children to adults
A math dictionary that you can keep at home and refer to for the rest of your life

"Dictionary of Mathematical Concepts: Understanding Through Pictures Without Memorization" introduces major mathematical concepts from each era, from prehistoric times to the present, in order, and also conveys the stories of mathematicians who had a significant impact on the history of mathematics as niche knowledge.
If you read the book, you can grasp the basic concepts and even the 'flow' of mathematics.
The concepts that appear in elementary, middle, and high school textbooks are clearly connected.
However, since the textbook itself is segmented, it is not easy for a learner to look far ahead and draw the big picture.
It's like having to find your way through a map that's broken into countless pieces, pieces that are handed out at different times.
This book is highly recommended not only to students who are lost in the sophisticated world of mathematics, but also to adults who long for a world with clear answers.