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IIGWP

International Intensive Geometry Winter Program (IIGWP) 2026

Think Beyond Formulas. Discover the Beauty of Mathematical Proof.

Geometry is not merely a collection of figures and formulas. It is the foundation of logical thinking, mathematical reasoning, and intellectual creativity.

HEAD DIRECTOR'S GREETING

Dear Students and Parents,

It is my great pleasure to welcome you to the International Intensive Geometry Winter Program (IIGWP) 2026, organized by the International Mathematics Center (IMC).

Mathematics has long been recognized as one of humanity's greatest intellectual achievements. At its heart lies geometry—a discipline that has inspired mathematicians, scientists, philosophers, architects, and engineers for more than two thousand years. From Euclid's Elements to modern artificial intelligence, geometry continues to shape the way we understand the world.

Unfortunately, many students experience geometry as a collection of formulas to memorize and procedures to imitate. They learn how to solve familiar problems but rarely have the opportunity to discover why mathematical ideas are true or how elegant proofs are constructed.

At IMC, we believe that mathematics should be experienced differently.

Mathematics is not simply about obtaining the correct answer. It is about asking meaningful questions, constructing logical arguments, recognizing hidden structures, and developing the intellectual discipline required to solve unfamiliar problems.

This philosophy forms the foundation of the International Intensive Geometry Winter Program.

Rather than emphasizing memorization, IIGWP emphasizes understanding.

Rather than teaching isolated techniques, we develop mathematical reasoning.

Rather than encouraging students to imitate solutions, we guide them toward discovering ideas independently.

Throughout this program, students will explore the beauty of Euclidean geometry through rigorous yet accessible instruction. Beginning with fundamental geometric principles, they will gradually develop the ability to analyze complex relationships, construct complete mathematical proofs, and solve increasingly sophisticated problems.

The curriculum has been carefully designed to bridge the gap between school mathematics and introductory Olympiad geometry. Students will encounter classical geometric ideas that have challenged mathematicians for centuries, while learning the logical techniques necessary to approach them with confidence.

One of the defining characteristics of IIGWP is its emphasis on mathematical proof.

Proof is the language of mathematics.

It teaches students to justify every statement with precision, communicate ideas clearly, and distinguish between intuition and rigorous reasoning. These abilities extend far beyond mathematics itself; they become valuable tools for future studies in science, engineering, computer science, economics, and many other disciplines.

We also recognize that genuine learning requires perseverance.

Students may encounter problems that seem difficult at first. This is not a weakness of the curriculum—it is one of its greatest strengths.

True mathematical growth occurs when students think deeply, make mistakes, refine their reasoning, and eventually discover elegant solutions through their own efforts.

Our goal is not simply to teach geometry during ten instructional days.

Our goal is to cultivate independent thinkers who approach challenges with curiosity, confidence, and intellectual integrity.

Whether you are preparing for advanced mathematics courses, mathematics competitions, future scientific research, or simply wish to experience the beauty of mathematical thinking, we sincerely hope that IIGWP will become an important milestone in your academic journey.

We warmly welcome talented middle and high school students from around the world to join our international learning community this winter.

We look forward to learning with you.

Head Director

Shubhrangshu Dasgupta

ABOUT IIGWP

The International Intensive Geometry Winter Program (IIGWP) is a ten-day international online enrichment program designed for motivated middle and high school students who wish to develop a deeper understanding of Euclidean geometry and mathematical proof.

Unlike traditional geometry courses that primarily emphasize formulas and routine exercises, IIGWP focuses on developing logical reasoning, proof-writing ability, creative problem solving, and mathematical maturity.

The program provides a carefully structured progression from fundamental geometric concepts to introductory Olympiad-level geometry, enabling students to build both confidence and intellectual independence.

Students will explore classical geometric theorems, discover elegant relationships among geometric figures, and learn how mathematicians develop rigorous arguments.

Every lesson has been designed not only to teach mathematical content but also to strengthen analytical thinking and cultivate the habits of mind that characterize successful mathematicians.

WHY STUDY GEOMETRY?

Geometry is one of the oldest and most influential branches of mathematics.

For more than two millennia, geometry has served as the foundation for scientific discovery, engineering innovation, architectural design, computer graphics, robotics, astronomy, and countless other disciplines.

More importantly, geometry teaches students how to think.

When solving a geometric problem, students learn to

These intellectual skills remain valuable regardless of future technological advances, including the rapid development of artificial intelligence.

Students who master geometry do far more than solve problems.

They develop a disciplined and logical way of thinking that benefits every area of academic study.

WHY LEARN MATHEMATICAL PROOF?

One of the defining characteristics of mathematics is that every statement must be supported by logical reasoning.

Unlike many other disciplines, mathematics does not rely on opinion, authority, or intuition alone. Every theorem must be established through proof.

Learning mathematical proof is therefore much more than learning how to solve geometry problems.

It is an exercise in disciplined thinking.

Students learn how to distinguish assumptions from conclusions, identify valid logical arguments, recognize hidden relationships, and communicate complex ideas with precision.

These abilities extend well beyond mathematics.

Proof-based reasoning strengthens critical thinking, analytical writing, scientific investigation, engineering design, computer programming, economics, philosophy, and many other fields that require structured problem-solving.

In today's world, artificial intelligence can perform calculations and retrieve information almost instantly.

However, genuine mathematical reasoning—the ability to discover new ideas, construct original arguments, and justify conclusions logically—remains a uniquely human intellectual strength.

At IMC, we believe that proof is not simply an academic exercise.

It is one of the most effective ways to cultivate independent thinkers capable of solving challenging problems with confidence, creativity, and intellectual integrity.

WHY CHOOSE IIGWP?

The International Intensive Geometry Winter Program has been designed to provide students with an educational experience that extends far beyond a traditional geometry course.

Students who join IIGWP benefit from a curriculum that emphasizes both mathematical understanding and intellectual growth.

Proof-Based Learning

Rather than memorizing formulas, students learn to understand why mathematical statements are true and how rigorous proofs are constructed.

Olympiad-Oriented Thinking

Students are introduced to classical geometric techniques frequently used in mathematics competitions, allowing them to develop deeper problem-solving strategies beyond the school curriculum.

Logical Reasoning

Every lesson encourages students to analyze problems systematically, recognize patterns, and develop precise mathematical arguments.

Carefully Structured Curriculum

Concepts are introduced in a logical progression, allowing students to build strong foundations before exploring more advanced topics.

International Learning Environment

Students from different countries participate in the same program, creating an academically stimulating international community.

Independent Thinking

Assignments are designed to encourage exploration rather than imitation.

Students are expected to think critically and develop their own mathematical ideas.

Long-Term Academic Growth

The goal of IIGWP is not simply to improve examination performance but to cultivate mathematical habits of mind that will benefit students throughout their academic careers.

OUR CORE VALUES

At the International Mathematics Center, every academic program is guided by six fundamental values.

Intellectual Curiosity

Great mathematics begins with curiosity.

We encourage students to ask questions, investigate patterns, and enjoy the process of discovery.

Logical Reasoning

Students learn to justify every mathematical statement using clear and rigorous reasoning.

Mathematical Excellence

We believe excellence is achieved through consistent effort, careful thinking, and intellectual honesty.

Independent Learning

Students are encouraged to explore ideas independently rather than relying solely on memorization or provided solutions.

Academic Integrity

Honesty, responsibility, and respect for original work are essential principles of every IMC program.

Global Collaboration

Mathematics is an international language.

Our programs bring together talented students from different cultures who share a common passion for learning.

OUR EDUCATIONAL PHILOSOPHY

At IMC, we believe that education should inspire students to become thinkers rather than merely successful test takers.

For this reason, our programs are designed around several educational principles.

Students should understand mathematical ideas before applying formulas.

Students should develop confidence through exploration rather than memorization.

Students should learn to appreciate mistakes as valuable opportunities for deeper understanding.

Students should gradually become independent learners capable of solving unfamiliar problems without relying on step-by-step instructions.

Most importantly, students should experience the joy of discovering mathematics for themselves.

This philosophy influences every lecture, every assignment, and every problem included in the International Intensive Geometry Winter Program.

LEARNING OUTCOMES

By the end of the program, students will be able to

Beyond geometry itself, students will also strengthen the intellectual habits necessary for success in higher-level academic study.

WHO SHOULD APPLY?

The International Intensive Geometry Winter Program welcomes motivated students from around the world who are eager to deepen their understanding of mathematics.

This program is particularly suitable for

Previous Olympiad experience is not required.

Students should possess a strong interest in mathematics and a willingness to think carefully, work independently, and embrace intellectual challenges.

PROGRAM OVERVIEW

Program Name

International Intensive Geometry Winter Program (IIGWP) 2026

Organizer

International Mathematics Center (IMC)

Program Format

Fully Online (Recorded Video Lectures)

Program Duration

December 19 – December 31, 2026

Instructional Days

10 Days

No Classes

Daily Lecture Length

Approximately 60 minutes

Language of Instruction

English

Target Participants

Motivated Middle School and High School Students

Homework

Daily submission required

Certificate

Official IMC Certificate of Completion

DAILY LEARNING STRUCTURE

The International Intensive Geometry Winter Program has been carefully designed to promote consistent learning through a structured daily routine. Rather than overwhelming students with long lectures, the program emphasizes focused instruction followed by meaningful independent practice.

Each instructional day follows the structure below.

Step 1. Watch the Daily Lecture

Students begin by watching a professionally prepared recorded lecture of approximately 50–60 minutes. Each lecture introduces new concepts, important theorems, proof techniques, and representative examples.

Step 2. Review the Lesson

Students are encouraged to review their notes, revisit important definitions and theorems, and reflect on the logical ideas presented during the lecture before beginning the assignment.

Step 3. Complete the Daily Assignment

A carefully designed homework assignment accompanies each lecture.

Assignments are intended not merely to assess understanding but also to strengthen logical reasoning, proof-writing ability, and problem-solving skills.

Students are expected to submit their assignment within eight hours after completing the lecture.

Step 4. Independent Mathematical Thinking

Students are encouraged to spend additional time exploring alternative solutions, reviewing proofs, and thinking deeply about challenging problems.

Developing independent thinking is one of the primary goals of this program.

COMPLETE CURRICULUM

Day 1

Foundations of Euclidean Geometry

Topics

Learning Objectives

Students establish a rigorous foundation for the remainder of the program while learning how mathematicians communicate ideas through precise definitions and logical arguments.

Day 2

Triangle Congruence

Topics

Learning Objectives

Students learn how congruent triangles form the basis of numerous geometric proofs and develop techniques for identifying hidden congruent figures.

Day 3

Similarity

Topics

Learning Objectives

Students discover how similarity allows complicated geometric relationships to be simplified through proportional reasoning.

Day 4

Triangle Centers

Topics

Learning Objectives

Students investigate remarkable points inside triangles while learning several powerful theorems that frequently appear in advanced geometry.

Day 5

Classical Geometry Theorems

Topics

Learning Objectives

Students begin studying elegant techniques commonly used in Olympiad geometry to solve seemingly difficult problems through surprisingly simple ideas.

Day 6

Circle Geometry I

Topics

Learning Objectives

Students explore the rich geometric relationships arising from circles and learn several classical properties that appear frequently in mathematical competitions.

Day 7

Circle Geometry II

Topics

Learning Objectives

Students extend their understanding of circles through elegant theorems that connect algebraic relationships with geometric configurations.

Day 8

Area Methods and Geometric Transformations

Topics

Learning Objectives

Students discover alternative approaches to geometry by using area arguments and geometric transformations to simplify complex proofs.

Day 9

Advanced Geometry

Topics

Learning Objectives

Students integrate concepts from previous lessons while exploring sophisticated ideas frequently encountered in higher-level mathematics competitions.

Day 10

Comprehensive Review & Final Geometry Challenge

Topics

Learning Objectives

Students consolidate everything learned throughout the program and apply multiple techniques to solve challenging geometry problems requiring creativity, logical reasoning, and mathematical maturity.

ASSIGNMENTS & LEARNING EXPECTATIONS

Learning mathematics requires active participation.

Accordingly, every instructional day includes a homework assignment carefully designed to reinforce the concepts introduced in the lecture.

Assignments are intended to encourage students to think independently rather than imitate solutions.

Students are expected to:

Assignments should be submitted within eight hours after watching the lecture.

Late submissions may not receive full evaluation.

Students are encouraged to attempt every problem, even if they cannot complete all of them successfully.

At IMC, thoughtful effort and logical reasoning are valued as highly as obtaining the correct answer.

APPLICATION PERIOD

Round 1

August 4 – August 27, 2026

Round 2

September 3 – September 24, 2026

Round 3

October 2 – October 25, 2026

Final Round

November 30 – December 8, 2026

Applications received after the final deadline may not be considered.

Selection is competitive, and early application is strongly encouraged.

APPLICATION REQUIREMENTS

Applicants are required to submit a complete application package for admission to the International Intensive Geometry Winter Program (IIGWP) 2026.

To simplify the submission process, all required documents except the recommendation letter must be combined into one ZIP file.

Applications that are incomplete may not be reviewed.

REQUIRED DOCUMENTS

Please prepare the following materials.

1. Completed Application Form

Applicants must complete the official IIGWP Application Form in full.

Please ensure that all information is accurate before submission.

2. Academic Awards and Certificates

Applicants are encouraged to include copies of mathematics-related awards, competition certificates, academic achievements, or other accomplishments that demonstrate their interest in mathematics.

Submission of awards is recommended but not mandatory.

3. Geometry Problem Set

Applicants are required to complete the official IIGWP Geometry Problem Set.

The problem set allows the admissions committee to better understand each student's mathematical background and problem-solving ability.

Applicants are strongly encouraged to complete at least 60% of the problems.

Perfect completion is not expected, and students should not be discouraged by difficult questions.

The purpose of the problem set is to evaluate mathematical thinking rather than obtain perfect scores.

FILE SUBMISSION FORMAT

Please combine all required documents into one ZIP file.

Example:

IIGWP2026_John_Smith.zip

The ZIP file should include:

HOW TO SUBMIT

Please submit your application by email.

Email Address

admin@imc-impea.org

Please use the following email subject line:

IIGWP 2026 Application – Student Name

Applicants will receive a confirmation email after the application has been successfully received.

Application Form

RECOMMENDATION LETTER

A recommendation letter is required as part of the application process.

However, applicants should not upload or submit the recommendation letter themselves.

Instead, applicants simply provide the name and email address of one teacher, mentor, or academic advisor who knows their mathematical ability well.

After receiving the application, the International Mathematics Center will contact the recommender directly by email.

The recommendation letter must be submitted directly by the recommender.

This process helps ensure confidentiality and fairness during admissions review.

ADMISSIONS REVIEW

Applications are reviewed holistically.

The admissions committee considers several factors rather than relying solely on examination performance.

Evaluation may include:

Mathematical Curiosity

Evidence of genuine interest in mathematics.

Problem-Solving Ability

Performance on the Geometry Problem Set.

Academic Preparation

Previous coursework, mathematical experience, and academic achievements.

Recommendation Letter

Academic potential, motivation, and intellectual character described by the recommender.

Overall Motivation

The committee values students who demonstrate curiosity, perseverance, and enthusiasm for learning.

No single factor determines admission.

Each application is reviewed individually.

PROGRAM FEE

Program Fee

USD $1,370

The program fee includes:

Payment instructions will be provided to admitted students after acceptance.

CERTIFICATE OF COMPLETION

Students who successfully complete the program requirements will receive an official Certificate of Completion issued by the International Mathematics Center (IMC).

To qualify for the certificate, students should

The certificate recognizes successful completion of the International Intensive Geometry Winter Program and reflects the student's commitment to rigorous mathematical learning.

FREQUENTLY ASKED QUESTIONS (FAQ)

Who can apply?

Motivated middle school and high school students from any country are welcome to apply.

Is previous Olympiad experience required?

No.

Students only need a strong interest in mathematics and a willingness to learn.

Is the program difficult?

The program is designed to be academically challenging.

Students should expect to think carefully and solve unfamiliar problems.

However, lectures are structured so that motivated students can gradually build the necessary skills.

How long is each lecture?

Approximately 50–60 minutes.

Is homework required?

Yes.

Homework is an essential part of the learning process and should be submitted within eight hours after watching each lecture.

Are live classes included?

No.

The program consists of professionally recorded lectures, allowing students to study according to their own schedule.

Will solutions be provided?

Selected solutions and explanations may be provided when appropriate.

Students are encouraged to attempt problems independently before reviewing any solutions.

What language is used?

All lectures, assignments, and official materials are presented in English.

Will I receive a certificate?

Yes.

Students who successfully complete the program requirements will receive an official IMC Certificate of Completion.

Can high school students participate?

Absolutely.

The program is designed for both middle school and high school students interested in developing stronger geometric reasoning and proof-writing skills.

What if I cannot solve every homework problem?

That is completely acceptable.

Many assignments contain challenging problems intended to encourage deep thinking.

Students are encouraged to make sincere attempts and explain their reasoning whenever possible.

At IMC, learning is valued more highly than perfection.

MESSAGE TO PARENTS

Dear Parents,

Thank you for considering the International Intensive Geometry Winter Program (IIGWP) 2026 for your child.

At the International Mathematics Center (IMC), we recognize that every parent hopes to provide educational experiences that inspire lasting intellectual growth rather than short-term academic success alone.

Today's students live in a world where information is instantly accessible. Artificial intelligence can answer questions, perform calculations, and solve routine exercises within seconds.

In such an environment, the most valuable educational objective is no longer memorizing information—it is developing the ability to think.

The ability to analyze unfamiliar situations, construct logical arguments, solve challenging problems, and communicate ideas clearly will remain essential throughout your child's future education and career.

These are precisely the abilities that mathematics, and particularly geometry, can cultivate.

The International Intensive Geometry Winter Program has therefore been designed with a clear educational philosophy.

Our goal is not simply to teach geometric formulas.

Our goal is to develop disciplined thinkers.

Throughout this program, students will learn how to approach unfamiliar problems with patience, justify every mathematical statement with logical reasoning, and appreciate the elegance of rigorous proof.

They will encounter challenges.

They will occasionally struggle.

They may not solve every problem immediately.

Yet these experiences are an essential part of genuine mathematical growth.

We encourage students to embrace difficult problems, learn from mistakes, and gradually build confidence through perseverance.

Such habits extend far beyond mathematics and prepare students for future success in science, engineering, computer science, economics, medicine, and many other disciplines.

Above all, we hope that every participant finishes this program with a deeper appreciation for mathematics—not merely as a school subject, but as a beautiful way of thinking.

We sincerely appreciate your trust and look forward to welcoming your family to the International Mathematics Center.

OUR VISION

At the International Mathematics Center, our vision extends beyond preparing students for examinations or competitions.

We aspire to cultivate a new generation of mathematical thinkers who possess curiosity, creativity, resilience, and intellectual integrity.

We believe that mathematics provides one of the strongest foundations for understanding the modern world.

Whether students pursue careers in science, engineering, artificial intelligence, economics, medicine, architecture, or entirely different fields, the habits of logical reasoning developed through mathematics will continue to serve them throughout their lives.

Our long-term vision is to establish a truly global mathematical community where talented students from every country can learn together, exchange ideas, and inspire one another.

By encouraging rigorous thinking, international collaboration, and a lifelong love of learning, IMC hopes to contribute meaningfully to the future of mathematics education.

WHY IMC?

Students choose the International Mathematics Center because we emphasize not only what students learn, but how they learn.

International Perspective

Students become part of a worldwide community of young mathematicians who share a passion for learning.

Academic Excellence

Courses are designed with depth, rigor, and intellectual challenge while remaining accessible to motivated learners.

Proof-Based Education

We place strong emphasis on mathematical proof, logical reasoning, and conceptual understanding rather than memorization.

Long-Term Development

Our goal is to nurture independent thinkers who will continue growing far beyond the completion of the program.

Passion for Mathematics

We strive to help students discover that mathematics is not simply about obtaining correct answers—it is about exploring ideas, recognizing patterns, and appreciating elegant reasoning.

CONTACT

Email
admin@imc-impea.org

FINAL MESSAGE

Think Beyond Formulas. Discover the Beauty of Mathematical Proof.

The International Intensive Geometry Winter Program is more than a winter course.

It is an opportunity to experience mathematics as mathematicians do—to ask questions, build logical arguments, solve elegant problems, and discover the beauty of rigorous thinking.

We warmly invite talented students from around the world to join us this winter and become part of an international community dedicated to mathematical excellence.

We look forward to welcoming you to IMC.