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CIT335Sciences3 Unitsintermediate

Computational Science and Numerical Methods

This course introduces students to computational science and numerical methods, essential for a Bachelor of Science in Computer Science degree. It covers topics such as machine numbers, computer arithmetic, and interpolation techniques. The course aims to develop a strong understanding of the principles underlying computational science, enabling students to solve problems related to machine arithmetic, number errors, and error analysis. Students will also learn about least square approximation and IEEE standards for floating-point arithmetic.

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200h

Study Time

13

Weeks

15h

Per Week

intermediate

Math Level

Course Keywords

Numerical MethodsComputer ArithmeticInterpolationError AnalysisApproximation

Course Overview

Everything you need to know about this course

Course Difficulty

Intermediate Level

Builds on foundational knowledge

65%

intermediate

📊

Math Level

Moderate Math

🔬

Learning Type

Hands-on Practice

Course Topics

Key areas covered in this course

1

Real Numbers and Machine Numbers

2

Floating-Point Arithmetic

3

Error Analysis

4

Condition Number

5

Least Square Approximation

6

Interpolation

7

IEEE Standard for Floating Point

Total Topics7 topics

Ready to Start

No specific requirements needed

This course is designed to be accessible to all students. You can start immediately without any prior knowledge or specific preparation.

Assessment Methods

How your progress will be evaluated (3 methods)

assignments

Comprehensive evaluation of course material understanding

Written Assessment

tutor-marked assessments

Comprehensive evaluation of course material understanding

Written Assessment

final examination

Comprehensive evaluation of course material understanding

Written Assessment

Career Opportunities

Explore the career paths this course opens up for you

Data Analyst

Apply your skills in this growing field

Software Developer

Apply your skills in this growing field

Numerical Analyst

Apply your skills in this growing field

Scientific Computing

Apply your skills in this growing field

Financial Modeler

Apply your skills in this growing field

Industry Applications

Real-world sectors where you can apply your knowledge

FinanceEngineeringScientific ResearchData ScienceComputer Graphics

Study Schedule Beta

A structured 13-week journey through the course content

Week

1

Module 1: Machine Arithmetic and Related Matter

3h

Unit 1: Real Number

3 study hours

•Read Unit 1: Introduction to Real Numbers, Machine Numbers, Fixed-Point Numbers, and Rounding.
•Understand the difference between real numbers and machine numbers.
•Practice converting real numbers to machine numbers and identifying rounding errors.

Week

2

Module 1: Machine Arithmetic and Related Matter

3h

Unit 2: Machine Arithmetic

3 study hours

•Study Unit 2: Learn about machine arithmetic, condition numbers, and the condition of a problem.
•Understand the model of machine arithmetic and error propagation.
•Solve problems involving arithmetic operations and error estimation.

Week

3

Module 1: Machine Arithmetic and Related Matter

6h

Unit 3: Condition Number

3 study hours

•Study Unit 3: Understand condition numbers and their significance in numerical analysis.
•Learn how to measure the sensitivity of a function to changes in input.
•Practice calculating condition numbers for simple functions.

Unit 4: Computer solution of a Problem

3 study hours

•Review Module 1 concepts.
•Work on assignments related to machine arithmetic and condition numbers.

Week

4

Module 2: Error Analysis and Computer Arithmetic

3h

Unit 1: Sources of Error

3 study hours

•Read Unit 1: Understand overall errors, sources of errors (input data, rounding, truncation), and basic concepts.
•Identify different types of errors in computational science.
•Practice estimating the size of errors in numerical computations.

Week

5

Module 2: Error Analysis and Computer Arithmetic

3h

Unit 2: Error Propagation

3 study hours

•Study Unit 2: Learn about error propagation in arithmetic operations.
•Understand how errors in data affect the results of computations.
•Solve problems involving error propagation in addition, subtraction, multiplication, and division.

Week

6

Module 2: Error Analysis and Computer Arithmetic

3h

Unit 3: Number Presentation

3 study hours

•Study Unit 3: Learn about number representation in computers.
•Understand rounding errors in floating-point representation.
•Practice converting numbers between different bases and estimating rounding errors.

Week

7

Module 2: Error Analysis and Computer Arithmetic

3h

Unit 4: Arithmetic Operations

3 study hours

•Study Unit 4: Understand arithmetic operations in computational science.
•Learn about floating-point addition, multiplication, and division.
•Practice performing arithmetic operations with floating-point numbers and estimating errors.

Week

8

Module 2: Error Analysis and Computer Arithmetic

3h

Unit 5: Accumulated Errors

3 study hours

•Study Unit 5: Learn about accumulated errors in computational science.
•Understand how errors accumulate in repeated floating-point operations.
•Solve problems involving error accumulation in summation and other operations.

Week

9

Module 2: Error Analysis and Computer Arithmetic

6h

Unit 6: IEEE Standard for Floating Point

3 study hours

•Study Unit 6: Understand the IEEE standard for floating-point arithmetic.
•Learn about different floating-point formats and their properties.
•Understand the implications of the IEEE standard for numerical computations.

Unit 7: IEEE Standard for Floating Point

3 study hours

•Review Module 2 concepts.
•Work on assignments related to error analysis and computer arithmetic.

Week

10

Module 3: Approximation and Interpolation

3h

Unit 1: Approximation and Interpolation: Overview

3 study hours

•Read Unit 1: Introduction to Approximation and Interpolation.
•Understand the general overview of the two concepts.
•Learn about the module overview.

Week

11

Module 3: Approximation and Interpolation

3h

Unit 2: Least Square Approximation

3 study hours

•Study Unit 2: Learn about least square approximation.
•Understand inner products and the normal equations.
•Solve problems involving least square approximation.

Week

12

Module 3: Approximation and Interpolation

6h

Unit 2: Least Square Approximation

6 study hours

•Review Module 3 concepts.
•Work on assignments related to approximation and interpolation.

Week

13

Module 3: Approximation and Interpolation

6h

Unit 2: Least Square Approximation

6 study hours

•Comprehensive review of all course materials.
•Focus on key concepts and problem-solving techniques.
•Prepare for final examinations.

This study schedule is in beta and may not be accurate. Please use it as a guide and consult the course outline for the most accurate information.

Course PDF Material

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Study Tips & Exam Preparation

Expert tips to help you succeed in this course

1

Focus on understanding the differences between real numbers and machine numbers, and how rounding errors occur during computations (Units 1-2).

2

Practice calculating condition numbers for various functions to assess their sensitivity to input changes (Unit 3).

3

Master the concepts of error propagation in arithmetic operations, paying close attention to cancellation errors (Unit 4).

4

Review the IEEE standard for floating-point arithmetic, including the different formats and their implications for accuracy (Unit 6).

5

Work through numerical examples of least square approximation to solidify your understanding of the method (Module 3).

6

Create concept maps linking error sources (Unit 1 Module 2) to error propagation (Unit 2 Module 2) and accumulated errors (Unit 5 Module 2).

7

Practice converting numbers between different bases (Unit 3 Module 2) and performing floating-point arithmetic operations (Unit 4 Module 2) without a calculator.

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