Math & Physics Course Calendar
• Weekly Sessions: We meet every Sunday for a 4-hour lesson.
• Course Duration: Runs for 7 weeks.
• Comprehensive Coverage: Focuses on all Math & Physics topics needed for your exam.
• Multiple Start Dates: Available 4 times a year – in October, December, February, and April (identical courses with different start dates).
October - November 2024
October 20th, 2024 - December 1st, 2024 - Sundays, 9:00 - 13:00 (Central European Time)
December - January 2024
December 15th, 2024 - January 26th, 2024 - Sundays, 9:00 - 13:00 (Central European Time)
February - March 2024
February 9th, 2024 - March 23rd, 2024 - Sundays, 9:00 - 13:00 (Central European Time)
April - May 2024
April 6th, 2024 - May 18th, 2024 - Sundays, 9:00 - 13:00 (Central European Time)
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Course Overview and Lesson Breakdown
Lesson 1:
Introduction to Basic Math and Set Theory
In this lesson, we will begin by exploring the foundation of mathematics through Set Theory. We will introduce essential symbols, definitions, and operations such as unions, intersections, and complements. Students will also learn about relations between sets and how to perform basic set operations. This understanding will provide the basis for tackling more complex mathematical concepts in the following lessons. By the end of the lesson, students will have a solid grasp of how sets are used to structure mathematical reasoning.
Understanding Number Sets and Equivalence Classes
This lesson dives into the world of numbers, from natural numbers to complex numbers. We will explore the basic operations of natural numbers, including divisibility, prime factors, and understanding M.C.D. and m.c.m. We will also discuss relative and rational numbers, focusing on operations and concepts like equivalent fractions, decimals, and percentages. The lesson will conclude with an introduction to real and complex numbers, highlighting the differences between rational and irrational numbers, and touching upon basic operations with complex numbers.
Lesson 2:
Operations Review and Advanced Mathematical Functions
In this lesson, we will review the essential operations, covering powers, roots, and their properties. We will extend the discussion to include exponential and logarithmic functions, introducing their definitions and fundamental properties. By reviewing these critical operations, students will build confidence and familiarity with mathematical tools that are necessary for problem-solving in more advanced topics, such as algebra and geometry.
Algebra Fundamentals and Polynomial Equations
Algebra is introduced in this lesson, starting with the basics of monomials and polynomials. Students will learn about their degree, operations, and how to find the M.C.D. and m.c.m. of polynomials. We will then move on to decomposing polynomials, identifying roots and zeroes. The lesson will also cover different types of equations, focusing on linear and quadratic equations, and introduce techniques for solving higher-degree equations. Finally, students will tackle algebraic fractions and understand conditions of existence (C.E.).
Lesson 3:
Analytic Geometry and Functions
This lesson will guide students through the fundamentals of Analytic Geometry, starting with the Cartesian plane and coordinate systems. Students will learn about distances, midpoints, and the properties of 1st and 2nd-degree curves, including lines, circles, ellipses, parabolas, and hyperbolas. We will also explore functions, introducing concepts like injective, surjective, and bijective functions, their domains, co-domains, and graphical representations. This lesson will help students visualize and analyze mathematical relationships in a geometric context.
Probability, Statistics, and Combinatorics
The final lesson introduces Probability and Statistics, starting with the definition of events and probability. Students will learn the difference between compatible and incompatible, dependent and independent events, and the main theorems of probability. We will also cover combinatorial calculus, focusing on permutations, combinations, and the binomial coefficient. In statistics, we will explore distributions, histograms, and measures like mode, median, and average. This lesson will provide students with the tools to analyze data and understand randomness in mathematical terms.
Lesson 4:
Follow up Test + Introduction to Core Concepts of Physics
In this foundational lesson, we introduce the essential tools and concepts used throughout physics. We begin with an overview of the International System of Measurement Units (S.I.) and learn how to apply dimensional analysis, orders of magnitude, and scientific notation to solve problems. Students will also explore errors and uncertainties, gaining an understanding of absolute and relative (%) errors and the importance of significant figures in measurements. The second part of the lesson covers scalars and vectors, where students will learn definitions, basic operations, and how to decompose vectors. Finally, we will introduce the cross and scalar products of vectors, setting the stage for their application in future lessons.
Kinematics and Motion
This lesson delves into the study of motion. Starting with the concepts of point-like bodies and reference frames, students will learn how to describe motion, velocity, and acceleration through definitions, formulas, and graphical interpretation. We will cover various types of motion, including uniform straight motion, uniformly accelerated motion, free fall (a=g), and circular motion, with a focus on understanding angular velocity, frequency, and period. This lesson will provide a strong foundation for analyzing how objects move through space under various conditions.
Lesson 5:
Dynamics and Newtonian Laws
In this lesson, students will explore Newton’s Laws of Dynamics and their implications in different physical scenarios. We begin by discussing inertial reference frames and Galilean relativity, followed by Newton’s three laws of motion: inertia, force and acceleration (F=ma), and action-reaction pairs. We will apply these laws to various situations, such as inclined planes, understanding linear and angular momentum, torque, and the center of mass. This lesson also introduces the conservation laws of momentum and angular momentum, including practical applications like levers and equilibrium.
Work, Energy, and Conservation Laws
Building on the concepts of dynamics, this lesson explores how forces cause changes in energy. Students will learn the definitions of work (joules) and power (watts), and differentiate between conservative and dissipative forces. We will study kinetic and potential energy, focusing on the law of conservation of energy. The lesson also introduces collisions, both elastic and inelastic, emphasizing the principle of momentum conservation. By the end of this lesson, students will have a deeper understanding of how energy and forces interact in physical systems.
Lesson 6:
States of Matter and Fluid Mechanics
In this lesson, we explore the properties and behaviors of matter in different states—solids, liquids, and gases. We begin by defining volume, density, and pressure and discussing the temperature scales (Celsius and Kelvin). Students will learn about the phase changes of matter and the unique properties of each state, such as elasticity in solids, surface tension in liquids, and the kinetic theory of gases. We will also study the ideal gas law (PV=nRT) and phase change diagrams. In the second part of the lesson, we introduce fluid mechanics, including Pascal’s Law, Stevino’s Law, and Archimedes’ Principle, giving students the tools to analyze both static and dynamic fluids.
Thermodynamics
The final lesson introduces the principles of thermodynamics, starting with heat, temperature, and the relationship between calories and joules. Students will learn about heat capacity, specific heat, and the different methods of heat transfer. The lesson continues with an introduction to thermodynamic systems and PV diagrams, including state functions and thermodynamic cycles like Carnot cycles. We will conclude by exploring the first and second laws of thermodynamics, discussing engine efficiency and the concept of entropy. This lesson provides a comprehensive understanding of energy transfer and the fundamental principles governing thermal systems.
Lesson 7:
Conclusion
In this concluding session, we will administer a comprehensive practice test to assess the progress each student has made throughout the course. This test is designed to mirror the structure and difficulty of the entrance exam, ensuring students are familiar with the types of questions they will face. By solving this test, students will have the opportunity to apply the knowledge and skills acquired across all the lessons, from basic principles to advanced concepts.
After the test, we will review the results to evaluate each student’s understanding and overall improvement. This evaluation will highlight areas of strength as well as any lingering gaps in knowledge. If a student achieves a score above the minimum required for admission to PoliMi, it will indicate that they are well-prepared for the actual exam. However, if a student’s score falls short of the required mark, it will serve as an indicator that further study and practice are necessary. In this case, I will recommend additional lessons, targeted revision of weak areas, and further practice tests to ensure that each student can confidently meet the required standard for admission.
This final lesson is crucial in providing a clear measure of each student’s readiness, offering both a sense of accomplishment and a guide for any necessary steps to improve performance before the official exam.
Final Remarks and Why You Should Take This Course
What we offer through studyinitaly is a combination of experience and expertise from two different fields. We are a team of two individuals, one of us a civil engineer, both of us are architects and having successfully navigated the PoliMi entrance exam process ourselves. In fact, we didn’t just get through it—we excelled, with one of us ranking 9th overall.
Having been through this journey, we know firsthand what it takes to succeed in the PoliMi admissions process. Over the past five years, we’ve dedicated ourselves to tutoring students, and our experience has helped many of them achieve top scores. What sets us apart is that we use our unique insights to guide you through the specific challenges of the TIL Test. For example, we know how to spot patterns in the types of questions and topics that are most likely to appear. Should you spend more time mastering Newton’s laws or diving into fluid mechanics? Which topics require deep focus, and which ones can you prioritize less? This is the kind of strategic knowledge we bring to the table.
Our goal is to equip you with everything you need to confidently tackle the architectural entrance exam. With our guidance, you’ll learn how to study efficiently, focusing on the right areas, and making the most of your preparation time. We believe that with the right approach and support, like the one we provide at studyinitaly, you can significantly boost your chances of success.
Good luck on your journey to becoming an architecture student—together, we’ll make sure you’re prepared to excel!