Course Description:

The course covers topics on Euclidean Geometry. The topics are discussed using both the deductive and inductive methods to conjecture definitions, corollaries, postulates and theorems on plane and solid geometry

Topics

The role of this course in the attainment of USeP VMGO, IGA, PEO and GO

     VMGO

     Institutional Graduate Attributes

     Program Educational Outcomes

     Graduate Outcomes

     Foundations of Mathematics course

Line and Angle Relationships

  1. Common Sense and Reasoning
  2. Sets, Statements and Reasoning
  3. Informal Geometry and Measurement
  4. Early Definitions and Postulates
  5. Angles and their Relationships
  6. Introduction to Geometric Proof
  7. Relations and Perpendicular Lines
  8. Formal Proof of a Theorem

Polygons and Triangles

1.     Basic Concepts of triangle

2.     Angles in a Triangle

3.     Congruent Triangles

4.     Proving Triangle Congruence

5.     Corresponding Parts of Congruent Triangles are congruent

6.     Pythagorean Theorem and Special Right Triangles.

Parallel Lines

1.        The Parallel Postulate and Special Angles

-Parallel lines

2.        Euclidean Geometry

3.        Parallel lines cut by a transversal and special angle.

4.        Proving Lines Parallel

Similar Triangles

1.        Ratio, Rates and Proportion

2.        Similar Polygons

3.        Proving triangles similar

4.        Similarity in Right Triangle

5.        Area of similar polygons

 

Circles and Arc

1.           Circles and Related Segments and Angles

2.           More Angle measures in the Circle

3.           Line and Segment relationships in the Circle

4.           Arcs of a Circle

. Areas of Polygons and Circles

  1. Area and Initial Postulates
  2. Perimeter and Area of Polygons
  3. Regular Polygons and Area
  4. Circumference and Area of a Circle
  5. Areas of the sector of the circle.

Surfaces and Solids

1.        Prisms, Area and Volume

2.        Pyramids, Area and Volume

3.        Cylinders and Cones

4.        Polyhedrons and Spheres

Symmetry, Transformation and Vectors,

1.        Reflections and symmetric figures

2.     Rigid Motions: reflections and translation

3.     Rotations

4.     Vectors

Course Description:

The course introduces students to circular and trigonometric functions, trigonometric identities and to the polar coordinates system. The students then apply concepts in these topics to applications in problem-solving.

 

Topics

The role of this course in the attainment of USeP VMGO, IGA, PEO and GO

·         VMGO

·         Institutional Graduate Attributes (IGA)

·         Graduate Outcomes (GO)

Course Outcomes

Learning Evidences

Grading System

Review

 

TRIGONOMETRIC FUNCTIONS

 

·         Right Triangle Trigonometry

 

·         Trigonometric Functions

GRAPHS OF TRIGONOMETRIC FUNCTIONS

·         Graphs of Periodic Functions

 

·         Graphs of Tangent Function, Cotangent Function, Secant Function and Cosecant Function

TRIGONOMETRIC IDENTITIES

·         Fundamental identities

·         Sum and Difference Identities

·         Double Angle Identities

* Product-to-Sum and Sum-to-Product Identities

Midterm Examination

INVERSE OF THE TRIGONOMETRIC FUNCTIONS

·         Inverse Trigonometric Functions

·         Solving Trigonometric Equations

SOLUTIONS OF TRIANGLES

·         Solving Right Triangles

·         Solving Oblique Triangles

a.        Law of Sines

Law of Cosines

POLAR COORDINATE SYSTEM

 

·         Conversion

-          Cartesian to Polar points and vice versa

-          Cartesian to Polar equations and vice versa

-          Graphing Polar points and functions

-          Distance between polar points.

This course deals with nature of mathematics, appreciation of its practical, intellectual, and aesthetic dimensions, and application of mathematical tools in daily life.

 The course begins with an introduction to the nature of mathematics as an exploration of patterns (in nature and environment) and as an application of inductive and deductive reasoning.  By exploring these topics, students are encouraged to go beyond the typical understanding of mathematics as merely a set of formulas but as a source of aesthetic in patterns of nature, for example, and a rich language in itself (and of science) governed by logic and reasoning.

 The course then proceeds to survey ways in which mathematics provides a tool for understanding and dealing with various aspects of present-day living, such as managing personal finances, making social choices, appreciating geometric design, understanding codes used in data transmission and security, and dividing limited resources fairly.  These aspects will provide opportunities for actually doing mathematics in a broad range of exercises that bring out the various dimensions of mathematics as a way of knowing, and test the students’ understanding and capacity. (CMO No. 20, series of 2013)