Remainder does not seem to be a big topic in school math. However, in competition math, it is. Almost every contest at middle school and high school level has remainder related problems. For example, in 2017 AMC 10B, out of total 25 problems, at least 3 are related to this topic: the 14th, 23rd, and 25th.

Modular arithmetic is a branch in mathematics which studies remainders and tackles related problems. However, this important subject is not taught in schools. Consequently, many students rely on their intuition when attempting to solve such problems. This is clearly not the best situation.

This book aims to provide a complete coverage of this topic at the level which is suitable for middle school and high school students. Contents will include both theoretical knowledge and practical techniques. Therefore, upon completion, students will have a solid skill base to solve related problems in math competitions.

Practice makes perfect. This book contains over 150 MOD related problems with complete solutions aiming to polish students' competition skills. It also contains a review chapter which highlights all the important concepts, theorems and techniques.It is recommended that reader should use this book together with the book Number Theory (MOD) which is also part of the Math All Star series.

Algebraic problems present a significant portion in all math competitions including MathCounts, AMC, AIME, USAMO and so on. Therefore, solving competition level algebraic problems is a must-master skills for every contest contender.

Though algebra is taught throughout middle and high schools, many useful techniques are left out. Taking Vieta's theorem as an example. While many students knows how to evaluate expressions such as $x_1^2+x_2^2$, they will need to learn additional methods in order to effectively evaluate higher power expression such as $x_1^{7}+x_2^{7}$, or asymmetric such as $5x_1^3 + 3 x_2^5$. In addition to expression evaluation, Vieta's theorem can also be used to solve some seemingly unrelated problems. Therefore, merely knowing the school way to use Vieta's theorem is far from being competition ready. This book will teach students many additional ways to utilize this theorem so that they will be able to use it in the best way.

Sequence is another example. A competent student should be able to use sequence to solve some seemingly unrelated problems, such as equations, trigonometry, complex numbers etc. All these are not taught in classrooms.

The goal of this book is to give in-depth discussion on various competition specific algebric techniques. They can be used either on their own or as steppingstones to solve complex problems. Nevertherless, mastering these techniques will surely lay down a solid foundation for students to achieve high in various math compettions..

Being able to calculate correctly and efficiently is one of the most basic but important math skills. Therefore, it is not surprising to see various calculation problems in competitions at all levels.

This book focuses on calculation skills. Contents are grouped by lectures. Each lecture features a classic problem. Many of such problems are not too hard to solve. However being able to solve these particular problems is just the very first step. It is more important to understand and master relevant calculation techniques. These techniques can help solve various problems of similar nature that will for sure appear in future math competitions.

Readers should have basic algebraic knowledge and skills in order to appreciate the contents in this book. Some problems involve trigonometry and complex number. They can be safely skipped by those students who are not familiar with these two subjects. Skipping certain topics will not affect learning other techniques contained in this book.

An indeterminate equation rises when the number of unknown variables exceeds the number of given equations. Solving indeterminate equations is a popular subject in math competitions at all levels, from AMC 8 to IMO. For example, in 2015 alone, both IMO and USAMO have one indeterminate equation problem out of the total six problems. Meanwhile, AIME and AMC12/10/8 also have various related questions.

However, how to solve indeterminate equations is rarely discussed in classrooms. As a result, many students are lack of the necessary knowledge and skills to tackle such problems. This book is to discuss various types of indeterminate equations and their corresponding solving techniques. Upon completing this book, readers should be able to recognize and solve these indeterminate equations comfortably.

You think everybody can count? Take a look at some counting problems in the practice section, and you might just think differently.

Counting problems appear in all levels of math competitions. It is one type of problems that senior students and even adults may not necessarily do better than well-trained junior students. This is because counting problems usually do not involve complex theorems or formulas. Rather, they demand a systematic and analytical approach.

The first half of the book teaches essential counting principles and formulas by going over easy-to-follow examples. After identifying hidden pitfalls and common misunderstandings, this book offers tips on how to avoid those traps. The second half covers well-established patterns in counting problems and introduces different ways to tackle each type. Mastering these techniques has proven to be very powerful and effective in improving problem solving skills.

This is not the second edition of the book Counting. Instead, it contains topics which are built upon the contents discussed in the first book. Generally speaking, this book targets AIME, national and international level competitions. Some techniques are quite advanced.

Techniques discussed in this book include bijection, recursion, counting integer solutions (balls-in-boxes), combinatorial identity, binomial/multinomial expansion, generating functions etc. Some examples and practice problems are at national and international math competition levels.

Practice makes perfect. This book contains about 100 problems focusing on binomial expansion (including multinomial expansion) and combinatorial identities (such as hockey stick identity, Vandermonde identity and so on). In addition to introducing these theorems and identities themselves, this book also discusses various typical problems and techniques that are related to these two topics.

Competition math is not all about complicated theorems and formulas. The ability to think logically and creatively plays an important role in solving challenging problems.

This book introduces some well-known methods of proof and aims to help improve students' ability to think effectively. Contents in this book are organized based on methodologies rather than specific subjects. Consequently, examples and practice problems presented in each chapter may cover many different subjects. For example, the chapter Symmetry covers polynomial factorization, equation, counting, and so on. All these problems in different subjects can be solved by exploiting their intrinsic symmetry properties. Developing such insights can help students to meaningfully improve their competion problem solving skills.

Additionally, some problems in this book originate from job interviews and other sources. Hence, mastering the art of thinking not only helps improving students' contest performance during school years, but also has positive impacts on their future.

Solving competition geometry problems is challenging. It requires students not only to remember lots of geometry theorems, but also to master various related techniques.

Though related, these two skills are not the same. Many geometry techniques are intuitive to apply. However, it can be surprisingly more effective to utilize these techniques than to solely rely on a bunch of theorems. Therefore, being proficient in employing appropriate techniques will boost one's problem solving ability in a meaningful way. That being said, the vast majority of math trainings and materials focus on teaching students geometry theorems.

This book will introduce a collection of geometry techniques which can be readily used to solve many competition geometry problems at various levels. Mastering them is a must for anyone who wants to be a strong contender in math competitions.

There are literally hundreds of, if not more, geometry theorems. Instead of attempting remembering all these theorems, students should focus on those most important and frequently used ones. Meanwhile, students should also be able to recognize typical patterns of applying these theorems. This book covers both areas.

Each chapter introduces a collection of related theorems. Those essential ones are discussed first. Students must remember all of them. Additional useful theorems are included in practice. They are good to know and remember. Examples and practices are intended to demonstrate these theorems' typical applications. Many of them are classic ones. Their conclusions are well-known and may be practically treated as theorems. As such, students are encouraged to remember such conclusions as well.

Trigonometry involves many formulas. It is practically impossible and often unnecessary to remember all of these formulas. Meanwhile, just remembering these formulas is not sufficient to become a strong competition contender. Therefore, it is critical to identify and remember those essential formulas. The first goal of this book is exactly to help students to achive this.

The second goal of this book is to coach students how to pick up the most appropriate formulas to solve given problems. Many trignometric problems can be solved using different formulas with different level of complexities. Hence, the ability to choose the most suitable formula is an important skills to develop.

Additionally, trigonometry is related to many other subjects such as geometry, complex number and so on. The book Geometry Techniques covers using trigonometric methods to solve geometry problems. This book also discusses how to use trigonometry to solve complex number problems, and vice versa.

This book is not intended to replace an 1000-page textbook which gives detailed lectures on every aspect of calculus. Instead, it is intended to explain core concepts in an intuitive way and to focus on practical perspectives of learning calculus.

First, this book emphasizes on computational skills. The vast majority of students will use calculus as a computational tool in various scientific areas such as mathematics, physics, engineering, computer science, quantitative finance, and so on. Therefore, being able to correctly and quickly calculate derivatives, integrals etc is extremely useful and important to these students. Many calculus theorems are also covered. However, those overly abstract and academical details will be kept to a minimal. Such contents are very important to those students who are interested in pursuing pure mathematics. However, focusing too much on these topics may be a distraction to most other students.

Another feature of this book is its focus on relations between calculus and various high school computational techniques such as trigonometric identities, polynomial transformation, and so on. Proficiency in using these techniques plays a vital role in solving many calculus problems. While these methods and formulas will be included in this book when they are needed, it is strongly recommended that readers should review these topics before attempting this book. Discussion of these techniques can be found in some Math All Star series books such as \textit{Power Calculation}, \textit{Trigonometry}, \textit{Competition Algebra}, and so on.

Meanwhile, this book also includes many examples and applications in various subjects which use calculus. These include continuous compounded interest in finance, root finding algorithm in computer science, optimization in machine learning, and of course various applications in physics. This will help prepare students for applying their calculus skills in their future study and career.

Finally, some selective historical competition problems are also included. These exercises provide students at different levels with an opportunity to test their problems solving skills that suit their individualized learning objective. Full solutions with detailed explanations are included.

Trading stock options is more versatile than trading stocks. Options offer a more predictable way to generate sustainable income. Unlike stock trading, which primarily relies on correctly predicting the movement of stock prices, stock options allow traders to not only profit from changes in stock prices but also from the lapse of time or changes in price volatility. Option traders can even make money when the stock price remains stable and unchanged. However, all of these opportunities require more than just intuition and a buy-low-sell-high mindset.

This book uniquely focuses on the practical aspects of options trading. It explains necessary technical details in an accessible manner, without requiring a background in advanced mathematics or finance subjects. Additionally, it delves into topics like understanding margin requirements, which is crucial for successful options trading and rarely covered in other books.

By the end of this book, readers will have acquired the essential theoretical and practical knowledge to begin trading stock options.

Solving brain teasers is fun. It is an interesting and engaging activity for a variety of occasions. Being good at solving brain teasers can make one more popular socially and more competitive career-wise. This is because such people are perceived as intrinsically more intelligent and interesting. As a matter of fact, many job interviews also test one's ability to solve brain teasers. Some interviews are entirely made up of them.This book contains 100 selective brain teasers representing a variety of typical types. What makes this book unique is that it does not simply list problems and give answers. Instead, this book aims to help improve your brain teaser solving skills. This first chapter of this book introduces different types of brain teasers and their corresponding solving techniques. It also provides advice on what to do and what to avoid. With these in mind, readers can start practice. Many of these problems are very typical. Some of them are coming from real tests and interviews. All problems come with answers. What will be more important is that detailed analysis and relevant notes are also included. They focus on explaining how solutions are derived, where are the traps and what are the hints found in these problems. These will surely help readers to improve their solving skills and become brain teaser masters.