Composition: Text + Commentary = 2 volumes wrapped

Part 1 (294 pages of the main text + 148 pages of commentary)

Chapter 1: Fundamentals of Mathematical Reasoning

1.
Answer sheet writing method and symbols
2. Tips for writing answers
3.
Mathematical reasoning study tips
4.
Solve real-world problems

Chp.2 Comprehensive coverage of geometric properties

1.
A complete summary of middle school geometric properties
2.
A complete summary of geometric properties for mathematical reasoning
3.
Solve real-world problems

Chp.3 Trigonometric Functions and Applications

1.
Several basic formulas of trigonometric functions
2.
Extension of special angles of trigonometric functions
3.
Relationship between sine and cosine functions
4.
Basics of the Law of Sines and the Law of Cosines
5.
Applications of the law of sines and cosines
6.
Solve real-world problems

Chp.4 Sequences & Applications of Sigma

1.
Attitude toward sequences and recurrence relation
2. How to determine the maximum/minimum of a sequence
3.
Various uses of sigma
4.
Solve real-world problems

Chp.5 Various proof methods

1.
Direct and indirect proof methods
2. Basics and Precautions of Mathematical Induction
3.
Application of mathematical induction
4.
Basics and Precautions of the Law of Absurdity
5.
Basics of the Daewoo Law
6.
Solve real-world problems

Chapter 6: Additional High-Difficulty Topics

1.
High-Difficulty Additional Topic Guide
2.
Solve difficult additional topics

Chp.7 Latest Past Questions

1.
The Standard of Mathematical Reasoning U-Base, the Show and Prove Series

From medical math essays at various universities to math essays at mid- to upper-tier universities, this series contains essential math essay concepts and problem-solving ideas for anyone who needs to solve recent Korean math essay problems.
The standard for the Mathematical Reasoning U-Base is whether you know most of the content of the Show and Prove series.

2.
Anyone can study.

Because the basics, applications, and advanced math essays are divided into chapters, readers can study in a customized manner according to their target university.

The author's recommended learning method is as follows:

Medical/Ointment Aspirants: All content is recommended.
Aspiring to top-tier universities: Optional study of high-difficulty topics (remaining content: recommended study)
Applicants for upper-middle-tier universities: Optional study of each unit's topics (excluding difficult topics: recommended study)

3.
The ultimate math entrance exam problem-solving guide, with helpful explanations and tips.

The author, who scored 100 points on the National College Scholastic Ability Test (NCSAT) math section 5 times and passed the math essay section (mathematics section) 6 times (including the top score in all science and engineering departments), shares problem-solving ideas and approaches for each frequently appearing type, which will lower the perceived difficulty of math essay section, which was previously perceived as difficult.

4.
Even as the years change, this book will always be your partner in mathematical reasoning studies.


Because this book contains the essence of mathematical reasoning, it is not only well-structured but also provides additional access to past exam questions that appear after publication through QR codes within the textbook.

5.
Unique textbook curriculum

The SaP series is designed to faithfully divide the concepts of upper-level mathematics into series, allowing students to quickly enter mathematical reasoning even when they are still struggling with calculus.
As the series progresses, the range of questions covered increases, making it much easier for students to understand the content of the series.

Show and Prove Mathematical Reasoning Series Curriculum Lineup

Part 1: Basic Logic & Mathematics for Mathematical Reasoning 1
Part 2: Math 2 & Calculus for Mathematical Reasoning
Advanced Calculus & Advanced Theme for Mathematical Reasoning, Part 3
Part 4: Elective Geometry and Elective Probability for Mathematical Reasoning (for students only)

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 & 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.