Exemptions are only available to SPMS students. Students from other schools are not eligible.
| Course | Exemption Criteria |
|---|---|
MAS 110 - Introduction to Scientific Programming |
All students: Those with adequate knowledge and experience with programming in C++ (cf. the syllabus) may apply to take the Exemption Test. Exemption is granted to those who pass the Exemption Test. (See section on Exemption Test.) |
MAS 111 - Foundations of Mathematics |
Direct exemption: International Mathematical Olympiad Medalist/Honorable Mention may be granted exemption without having to take the Exemption Test. Through Exemption Test: Students who meet any of the following conditions may apply to take the Exemption Test. Exemption for this Course is granted to those who pass the Exemption Test. (See section on Exemption Test.) A level candidates: Students with grade ‘A’ in Further Mathematics or Distinction in S-paper for Mathematics. Polytechnic candidates: Students who have passed advanced mathematics Courses beyond the standard curriculum (e.g., CEM in SP, Advanced Engineering Mathematics at NP, etc). Others: Students who have the equivalent of grade ‘A’ in A Level Further Mathematics or Distinction in S-paper in Mathematics. |
MAS 112 - Calculus I |
Direct exemption: International Mathematical Olympiad Medalist/Honorable Mention may be granted exemption without having to take the Exemption Test. Through Exemption Test: Students who meet any of the following conditions may apply to take the Exemption Test. Exemption for this Course is granted to those who pass the Exemption Test. (See section on Exemption Test.) A level candidates: Students with grade ‘A’ in Further Mathematics or Distinction in S-paper for Mathematics. Polytechnic candidates: Students who have passed advanced mathematics Courses beyond the standard curriculum (e.g., CEM in SP, Advanced Engineering Mathematics at NP, etc). Others: Students who have the equivalent of grade ‘A’ in A Level Further Mathematics or Distinction in S-paper in Mathematics. |
MAS 113 - Calculus II |
Direct exemption: International Mathematical Olympiad Medalist/Honorable Mention may be granted exemption without having to take the Exemption Test. Through Exemption Test: Students who meet any of the following conditions may apply to take the Exemption Test. Exemption for this Course is granted to those who pass the Exemption Test. (See section on Exemption Test.) A level candidates: Students with grade ‘A’ in Further Mathematics or Distinction in S-paper for Mathematics. Polytechnic candidates: Students who have passed advanced mathematics Courses beyond the standard curriculum (e.g., CEM in SP, Advanced Engineering Mathematics at NP, etc). Others: Students who have the equivalent of grade ‘A’ in A Level Further Mathematics or Distinction in S-paper in Mathematics. |
MAS 114 - Linear Algebra I |
Direct exemption: International Mathematical Olympiad Medalist/Honorable Mention may be granted exemption without having to take the Exemption Test. Through Exemption Test: Students who meet any of the following conditions may apply to take the Exemption Test. Exemption for this Course is granted to those who pass the Exemption Test. (See section on Exemption Test.) A level candidates: Students with grade ‘A’ in Further Mathematics or Distinction in S-paper for Mathematics. Polytechnic candidates: Students who have passed advanced mathematics Courses beyond the standard curriculum (e.g., CEM in SP, Advanced Engineering Mathematics at NP, etc). Others: Students who have the equivalent of grade ‘A’ in A Level Further Mathematics or Distinction in S-paper in Mathematics. |
MAS 181 - Calculus for the Sciences I |
Direct exemption: Students who meet any of the following conditions may be granted exemption without having to take the Exemption Test: (i) grade ‘A’ in A Level Further Mathematics or Distinction in S-paper for Mathematics, or (ii) International Mathematical Olympiad Medalist/Honorable Mention. Through Exemption Test: Students who meet any of the following conditions may apply to take the Exemption Test. Exemption for this Course is granted to those who pass the Exemption Test. (See section on Exemption Test.) Polytechnic candidates: Students who have passed advanced mathematics Courses beyond the standard curriculum (e.g., CEM in SP, Advanced Engineering Mathematics at NP, etc). Others: Students who have the equivalent of grade ‘A’ in A Level Further Mathematics or Distinction in S-paper in Mathematics. |
MAS 182 - Calculus for the Sciences II |
Direct exemption: Students who meet any of the following conditions may be granted exemption without having to take the Exemption Test: (i) grade ‘A’ in A Level Further Mathematics or Distinction in S-paper for Mathematics, or (ii) International Mathematical Olympiad Medalist/Honorable Mention. Through Exemption Test: Students who meet any of the following conditions may apply to take the Exemption Test. Exemption for this Course is granted to those who pass the Exemption Test. (See section on Exemption Test.) Polytechnic candidates: Students who have passed advanced mathematics Courses beyond the standard curriculum (e.g., CEM in SP, Advanced Engineering Mathematics at NP, etc). Others: Students who have the equivalent of grade ‘A’ in A Level Further Mathematics or Distinction in S-paper in Mathematics. |
MAS 801 - It’s a Discreetly Discrete World: Mathematics in Real-Life Applications |
Direct exemption: Students who meet any of the following conditions may be granted exemption without having to take the Exemption Test: (i) grade ‘A’ in A Level Further Mathematics or Distinction in S-paper for Mathematics, or equivalent, or (ii) International Mathematical Olympiad Medalist/Honorable Mention. |
MAS 802 - Tackling the Odds: Inside Statistics |
Direct exemption: Students who meet any of the following conditions may be granted exemption without having to take the Exemption Test: (i) grade ‘A’ in A Level Mathematics or Further Mathematics, or Merit or Distinction in S-paper for Mathematics, or equivalent, or (ii) International Mathematical Olympiad Medalist/Honorable Mention. |
Exemption tests for MAS 110, 111, 112, 113, 114, 181 and 182 will be held in July, before SPMS students matriculate. Candidates for the Exemption Tests will be informed of the dates in due course.
The test for each Course will be based on the syllabus for the Course. For details, please refer to the section on Syllabi for Exemption Tests. The standard prescribed for the Exemption Tests is comparable to that for the Final Examination of the corresponding Course, except that the Exemption Test is a 1-hour test while the usual Final Examination lasts for 2.5 hours. The Final Examinations of these Courses in AY 2005/06 are available for the candidates’ reference:
The detailed syllabus of each Course, as well as a recommended textbook, is given below:
This is an introductory Course on scientific programming using Fortran and C/C++, intended primarily for students in physical and mathematical sciences. The objective is to equip the students with basic programming skills, including the use of existing libraries, useful in the study of physical and mathematical sciences. Fundamental concepts of programming. Brief overview of scientific programming languages (Fortran, C/C++). Basic data types, functions, classes, templates, STL (container classes, algorithms), memory management. Compilation process, use of existing C/C++/Fortran libraries. Algorithmic problem solving and design process, program development, coding and debugging, fundamental programming constructs, data structures, recursions, simple file processing, algorithmic complexity. Case studies in physical and mathematical sciences.
Recommended Text:
John R. Hubbard, Schaum’s Outline of Theory and Problems of Programming with C++, 2nd Edition, McGraw Hill, (ISBN: 0-07-135346-1)
This Course introduces fundamental ideas and techniques used in many different areas of mathematics. Elementary logic, mathematical statements, quantified statements. Sets, operations on sets, Cartesian products, properties of sets. Natural numbers, integers, rational numbers, real numbers, complex numbers. Relations, equivalence relations, equivalence classes. Functions, injective and surjective functions, inverse functions, composition of functions. Mathematical proofs, mathematical induction.
Recommended Text:
Susanna S. Epp, Discrete Mathematics with Applications, 3rd Edition, Thomson Publishing (Brooks/Cole), (ISBN: 0-534-49096-4)
This is the first Course on calculus in a sequence of four Courses. The objective is to introduce basic notions of calculus and analytic geometry, including differentiation. Real numbers, functions and graphs, trigonometric functions. Limits of functions, continuity at a point, continuity on an interval. Differentiability, derivatives of functions, chain rule, implicit differentiation, derivatives of higher order. Local maxima and local minima, Rolle’s Theorem and Mean Value Theorem, points of inflection, first-derivative and second-derivative tests, Newton’s Method. Antidifferentiation.
Recommended Text:
James Stewart, Calculus, 5th Edition, Thomson Publishing (Brooks/Cole), (ISBN: 0-534-27408-0)
This is the second Course in the calculus sequence. The objective is to study integration and related topics. Indefinite and definite integrals, Mean Value Theorem for integrals, Fundamental Theorems of Calculus, area of plane regions. Volumes of solids, length of arcs, other applications of the definite integral. Inverse functions, logarithm functions, exponential functions. Inverse trigonometric functions, hyperbolic functions. Techniques of integration. Elementary differential equations.
Recommended Text:
James Stewart, Calculus, 5th Edition, Thomson Publishing (Brooks/Cole), (ISBN: 0-534-27408-0)
This is the first of two Courses on linear algebra. The main objective is to introduce basic notions in linear algebra that are often used in other areas of mathematics and applications. Systems of linear equations, Gaussian elimination. Matrices, inverses, determinants. Vectors, dot product, cross product. Vector spaces, subspaces, linear independence, basis, dimension, row and column spaces, rank.
Recommended Text:
Howard Anton & Chris Rorres, Elementary Linear Algebra with Applications, 9th Edition, Wiley, (ISBN: 0-471-66959-8)
This is the first of two Courses on calculus designed to equip students in the sciences with basic working knowledge of calculus. Applications and computer-based learning will be included. Functions and graphs, real numbers. Differentiation of functions of one variable, derivative as rate of change, chain rule, implicit functions, inverse functions. Local maxima and minima. Indefinite and definite integrals, applications of integration.
Methods of integration. Fundamental theorem of calculus.
Recommended Text:
James Stewart, Calculus, 5th Edition, Thomson Publishing (Brooks/Cole), (ISBN: 0-534-27408-0)
This second Course on calculus is designed to equip students in the sciences with knowledge of further topics in this useful tool for modern science and engineering. Differential equations – first-order and second-order linear differential equations. Techniques of solving differential equations, applications. Series and power series. Taylor’s series. Fourier series.
Recommended Text:
James Stewart, Calculus, 5th Edition, Thomson Publishing (Brooks/Cole), (ISBN: 0-534-27408-0)