CIT335

Computational Science and Numerical Methods

Sciences
300 level
3 credit units
102 pages
11 units

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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About this course

Difficulty: Intermediate
Study hours: 200 hours
Maths: Intermediate
Content: Theoretical, practical, problem solving
Practical work: Yes

How it is assessed

Assignments
Tutor marked assessments
Final examination

What you'll read

The real module and unit structure of CIT335, taken from the course material NOUN publishes.

Module 1

Module 2 · Error Analysis and Computer Arithmetic

Module 3 · Approximation and Interpolation

One paragraph, so you can see how it reads

CIT335 · Unit 1: Real Number

We begin with the number system commonly used in mathematical analysis and confront it with the more primitive number system available to us on any particular computer. We identify the basic constant (the machine precision) that determines the level of precision attainable on such computer.

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What you should be able to do

Explain the basic concepts of machine arithmetic and related matters.
Describe the basic problems in approximation theory.
Explain the notions behind condition number.
Identify the basic concepts of error analysis and computer arithmetic.
Discuss the underlying principles of least square approximation.

What it prepares you for

Careers

Data Analyst
Software Developer
Numerical Analyst
Scientific Computing
Financial Modeler

Where it is applied

Finance
Engineering
Scientific Research
Data Science
Computer Graphics

Where it gets hard

The units students slow down on, and what makes each one heavy.

Module 1: Machine Arithmetic and Related Matter
Unit 3: Condition Number
Understanding the nuances of condition number requires grasping the sensitivity of mathematical operations to small input changes, which can be conceptually challenging.
Module 2: Error Analysis and Computer Arithmetic
Unit 5: Accumulated Errors
Unit 5 requires understanding how individual rounding errors accumulate and propagate through multiple calculations, potentially leading to significant deviations from expected results.

A suggested way through it

Suggested

13 weeks, about 51 hours in total. Yours will differ.

Week 1Module 1: Machine Arithmetic and Related Matter
- Unit 1: Real Number · 3 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 2Module 1: Machine Arithmetic and Related Matter
- Unit 2: Machine Arithmetic · 3 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 3Module 1: Machine Arithmetic and Related Matter
- Unit 3: Condition Number · 3 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 hours
  Review Module 1 concepts.. Work on assignments related to machine arithmetic and condition numbers..
Week 4Module 2: Error Analysis and Computer Arithmetic
- Unit 1: Sources of Error · 3 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 5Module 2: Error Analysis and Computer Arithmetic
- Unit 2: Error Propagation · 3 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 6Module 2: Error Analysis and Computer Arithmetic
- Unit 3: Number Presentation · 3 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 7Module 2: Error Analysis and Computer Arithmetic
- Unit 4: Arithmetic Operations · 3 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 8Module 2: Error Analysis and Computer Arithmetic
- Unit 5: Accumulated Errors · 3 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 9Module 2: Error Analysis and Computer Arithmetic
- Unit 6: IEEE Standard for Floating Point · 3 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 hours
  Review Module 2 concepts.. Work on assignments related to error analysis and computer arithmetic..
Week 10Module 3: Approximation and Interpolation
- Unit 1: Approximation and Interpolation: Overview · 3 hours
  Read Unit 1: Introduction to Approximation and Interpolation.. Understand the general overview of the two concepts.. Learn about the module overview..
Week 11Module 3: Approximation and Interpolation
- Unit 2: Least Square Approximation · 3 hours
  Study Unit 2: Learn about least square approximation.. Understand inner products and the normal equations.. Solve problems involving least square approximation..
Week 12Module 3: Approximation and Interpolation
- Unit 2: Least Square Approximation · 6 hours
  Review Module 3 concepts.. Work on assignments related to approximation and interpolation..
Week 13Module 3: Approximation and Interpolation
- Unit 2: Least Square Approximation · 6 hours
  Comprehensive review of all course materials.. Focus on key concepts and problem-solving techniques.. Prepare for final examinations..

Preparing for the exam

What to do

Focus on understanding the differences between real numbers and machine numbers, and how rounding errors occur during computations (Units 1-2).
Practice calculating condition numbers for various functions to assess their sensitivity to input changes (Unit 3).
Master the concepts of error propagation in arithmetic operations, paying close attention to cancellation errors (Unit 4).
Review the IEEE standard for floating-point arithmetic, including the different formats and their implications for accuracy (Unit 6).
Work through numerical examples of least square approximation to solidify your understanding of the method (Module 3).
Create concept maps linking error sources (Unit 1 Module 2) to error propagation (Unit 2 Module 2) and accumulated errors (Unit 5 Module 2).
Practice converting numbers between different bases (Unit 3 Module 2) and performing floating-point arithmetic operations (Unit 4 Module 2) without a calculator.

Questions students ask about this course

What is CIT335 about?

How many units does CIT335 have?

CIT335, Computational Science and Numerical Methods, has 11 units across 3 modules, over 102 pages of course material. You can read it one unit at a time.

How many credit units is CIT335?

CIT335 carries 3 credit units, at 300 level in Sciences.

Is CIT335 hard?

CIT335 is rated intermediate level, with intermediate mathematical content. It is mostly theoretical, practical and problem solving work, and it has a practical component.

How long does CIT335 take to study?

About 200 hours of study, spread across its 11 units.

How is CIT335 assessed?

CIT335 is assessed by assignments, tutor marked assessments and final examination.

What can I do with CIT335?

Data Analyst, Software Developer, Numerical Analyst, Scientific Computing and Financial Modeler.