Chp.1 Introduction to Polynomial Functions
1.
Common properties of polynomial functions
2.
Properties and proof of quadratic functions
3.
Properties and proof of cubic functions
4.
Solve real-world problems

Chp.2 Limits and continuity of functions
1.
Basic understanding and calculation methods of extremes
2.
Sandwich Summary for Mathematical Reasoning
3.
continuity of functions
4.
Basics and Applications of the Max-Min Theorem
5.
Organizing and utilizing intermediate values
6.
Solve real-world problems

Chapter 3 Differentiation and its various applications
1.
Differentiability
2.
Various applications of differentiation
3.
The basics of the mean theorem
4.
Practical Tips for Applying the Mean Theorem
5.
Solve real-world problems

Chp.3.5 Time to take a break
1.
Concluding Show and Prove Part 2

Chapter 4: Additional High-Difficulty Topics
1.
High-Difficulty Additional Topic Guide
2.
Solve additional difficult questions

Chp.5 Latest Past Questions
1.
Solve the latest past exam questions

Book review

Lee Ji-hoon

〈show&prove〉 is a self-study book on mathematics that was a decisive help in passing the Yonsei University mathematics essay exam.
As a reader and a student, I believe that the paradigm of learning mathematical reasoning is divided into before and after Kim Ki-dae T's mathematical reasoning class.

Kim Ki-dae's philosophy for passing the math essay exam is to focus on "breaking the passing mark with a high probability" rather than "getting a high score with a low probability."
Rather than classes/textbooks that help you raise your high score, we aim for classes/textbooks that help you raise your low score above the passing score.

I believe that the latter class/textbook will be overwhelmingly more helpful to the majority of students than the former. I also reached the same conclusion during my preparation for the math essay exam, so I completely agree with his teaching method and believe that I was able to pass the Yonsei University math essay exam thanks to his efficient learning method.

This book is optimized to achieve the latter goal.
We will break away from the old method of simply solving past exam questions and looking at the explanations, and let you know that there is an 'approach' to mathematical reasoning.
It is structured to organize and practice core approaches by type, and in particular, the fact that the frequently appearing types of questions across universities are reorganized in order of difficulty will be of great help to test takers in achieving extreme efficiency within a limited time.


This book is highly recommended not only to students who are new to mathematical reasoning, but also to all test takers who have lost their way in mathematical reasoning by only repeating past exam questions.
There is a clear difference between knowing the direction and walking and arriving at a destination by chance.
This textbook will serve as a clear compass for your mathematical reasoning studies.

I sincerely hope that all test takers preparing for the math essay will show their skills through “Show & Prove” and ultimately prove them with results.


Jeon Jun-hyeon
Mathematical reasoning is not simply a test of guessing the correct answer.
The key is to accurately understand the intention of the examiner and to logically explain that intention using the language of mathematics.
This book offers clear solutions to help you develop that very ability.

This textbook teaches you how to think and logically connect mathematical reasoning problems using the core concepts of "conditions, change processes, and new facts."
This goes beyond simply memorizing the solution process; it allows you to train yourself to construct and weave a logical flow that leads to the answer.

If you're a student who feels overwhelmed by mathematical reasoning, this book will deepen your mathematical thinking and elevate your logical reasoning skills to the next level.
I strongly recommend that you fully decipher the examiner's intent and fill your answer sheet with flawless logic.

Park Min

I believe that Show and Prove is a textbook that systematically develops logical descriptive and proof skills from the ground up.
I think this is a friendly book written so that even students who are new to mathematical reasoning can study it without any burden.

This book is especially recommended for students who lack concepts, as it provides a good foundation for not only calculus but also mathematics I and mathematics upper and lower third.

Another great advantage is that it allows for personalized learning for learners by displaying the difficulty level for each problem.