Interactive Coursebook (Online) of C27 Mathematical Proofs
C27 Mathematical Proofs
What’s on the Specification
| Prf1 | Follow a proof of the following types, and in simple cases know how to construct such a proof.
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| Prf2 | Deduce implications from given statements. |
| Prf3 | Make conjectures based on small cases, and then justify these conjectures. |
| Prf4 | Rearrange a sequence of statements into the correct order to give a proof for a statement. |
| Prf5 | Problems requiring a sophisticated chain of reasoning to solve. |
| Err1 | Identifying errors in purported proofs. |
| Err2 | Be aware of common mathematical errors in purported proofs; for example, claiming ‘if \(ab = ac\), then \(b = c\)’ or assuming ‘if \(\sin A = \sin B\), then \(A = B\)’ neither of which are valid deductions. |
Learning Objectives
- Understand the nature and importance of mathematical proof.
- Construct and follow direct deductive proofs.
- Apply proof by cases (exhaustion) by dividing a problem into appropriate scenarios.
- Understand the logic of proof by contradiction and use it in simple cases.
- Know how to disprove a statement using a counterexample.
- Identify logical errors or common mathematical mistakes in purported proofs.
- Deduce implications and form chains of reasoning to solve proof-based problems.
Suggested Time
| Task | No. of Questions | Suggested Time |
|---|---|---|
| Examples | 7 | 170 min |
| Quiz | 4 | 10 min |
| Practice A | 10 | 30 min |
| Practice B | 12 | 30 min |
| Total | 33 | 3-4hrs |
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