MTE 2115 Applied Algebra Quiz

Course Overview

• Subject: MTE 2115 Applied Algebra
• No prerequisite required, making it accessible for all students.
• Intended to deepen understanding of algebraic laws and mathematical manipulation.

Learning Outcomes

• Ability to utilize linear laws for interpreting experimental data.
• Proficiency in solving problems involving finite and infinite power series.
• Skills in performing operations with complex numbers, specifically in relation to trigonometric identities.

Key Topics Covered

• Surds, Logarithms, and Indices: Representation and manipulation of radical expressions and logarithmic functions.

• Linear Laws: Determination from experimental data to model real-world phenomena.

• Quadratic Functions: Exploration of quadratic equations, graphs, and inequalities, including the Remainder Theorem for polynomial solutions.

• Permutations and Combinations: Fundamental concepts in counting techniques for discrete mathematics.

• Series: Understanding and applications of different types of series:

  • Finite and Infinite Series
  • Arithmetic Series (linear growth)
  • Geometric Series (exponential growth)
  • Binomial Series with practical applications such as compound interest calculations.

• Principle of Induction: Techniques for proving statements about integers, including summation formulas and divisibility properties.

• Trigonometry: Comprehensive study of:

  • Trigonometric functions and their graphs.
  • Degrees and radians for angle measurement.
  • Addition, multiple angle, and factor formulae for trigonometric identities and equations.
  • Application of sine and cosine formulas in solving triangles.

• Complex Numbers: Analyzing complex numbers through:

  • Argand diagrams for geometric representation.
  • Arithmetic operations involved with complex numbers.
  • Understanding modulus and argument.
  • De Moivre's Theorem, including applications in trigonometric identities and extraction of complex roots.

Teaching Methodology

• Instruction primarily through lectures, supplemented by tutorials and group discussions for collaborative learning.

Assessment Structure

• Continuous Assessment Tests to gauge understanding throughout the course.
• End of Semester Examination contributing 70% towards final grade, with continuous assessments accounting for the remaining 30%.

Instructional Materials

• Utilization of Liquid Crystal Displays for presentations and demonstrations.
• Whiteboards/blackboards for interactive problem-solving and explanations.

Test your knowledge on the fundamental laws of algebra, including series and complex numbers. This quiz aims to assess your ability to solve problems involving finite and infinite power series and apply complex number operations in trigonometry. Perfect for students looking to enhance their algebra skills.