Applied Mathematics - Mathematical Reasoning

🎉 Dive into the World of Applied Mathematics with our "Mathematical Reasoning" Course! 🎓

Course Instructor: Studi Livecourse

Unlock the Secrets of Success in Math: Master Key Exams Like IIT-JEE Main & Advanced, BITSAT, SAT, MSAT, MCAT, and More!

Welcome to the "Mathematical Reasoning" course, your gateway to understanding and excelling in some of the most challenging math competitions out there – IIT-JEE Main & Advanced, BITSAT, SAT, MSAT, MCAT, and state board exams including CBSE, ICSE, IGCSE, and beyond!

Course Overview:

Mathematical Reasoning 🔍

• Understanding Statements:

  • Mathematically Acceptable Statements: We'll delve into what makes a statement true or false, and why it matters.

• Mastering Connecting Words:

  • Learn the nuances of "if and only if (necessary and sufficient conditions)," "implies," "and/or," "implied by," "and," "or," and "there exists." We'll reinforce your understanding with real-life examples and mathematical scenarios.

• Validating Statements:

  • Grasp the difference between contradiction, converse, and contrapositive in compound statements and learn how to validate them effectively.

Key Takeaways from the Course:

1. Mathematically Acceptable Statements: A statement is either true or false, and understanding this is fundamental to mathematical reasoning.

2. Exploring Logical Terms:

   • Negation of a Statement: We'll cover how to negate a statement and what ∼p means.
   • Compound Statements: Learn about the components that make up complex statements.
   • Quantifiers “And,” “Or”: Understand the role these play in compound statements.
   • Implications: “If,” “Only If,” and their implications. We'll break down how to express a sentence with implication, including its sufficiency for a conclusion and its necessity as a condition.

3. Contrapositive & Converse:

   • Discover the significance of the contrapositive and converse in proving statements.
   • Learn how a statement p ⇒ q is related to its converse q ⇒ p and the role they play together.

Validity Checks:

To ensure the robustness of your reasoning, we'll explore four main methods for checking the validity of statements:

• (i) Direct Method: A straightforward approach to prove a statement is true by showing that its components are true.
• (ii) Contrapositive Method: Prove the contrapositive of a statement to demonstrate the original statement's validity.
• (iii) Method of Contradiction: Assume the opposite of what you want to prove and show that this leads to a contradiction.
• (iv) Using a Counter Example: Disprove a statement by finding a single case where it does not hold true.

Join Us on This Mathematical Adventure!

Whether you're aiming to ace your state board exams, conquer the IIT-JEE, BITSAT, SAT, MSAT, MCAT, or simply want to hone your mathematical reasoning skills, this course is tailored to help you achieve your goals. With a focus on clear explanations and practical application, you'll not only understand the concepts but also be able to apply them effectively in high-stakes examinations.

Enroll now and take the first step towards mastering Mathematical Reasoning! 🌟