FIT1058 Foundations of Computing
The Complete Exam Bible · S2 2026FIT1058 Overview
- Monash Faculty of Information Technology
- Semester 2, 2026
- an undergraduate foundation computing unit
- 6 credit points
- a discrete foundations unit for computing
FIT1058 covers sets, functions, relations, proof, propositional and predicate logic, sequences, counting, number theory, discrete probability and graph theory. It is taught within Monash Faculty of Information Technology. It is an undergraduate foundation computing unit. It carries 6 credit points.
- Domain before truth A statement's meaning and truth depend on the declared universe.
- Examples do not prove universals One counterexample can refute a universal; examples alone cannot establish it.
- Counting needs a sample space Addition, multiplication and probability rules depend on mutually exclusive or independent structure.
- Three thresholds apply Final, in-semester and overall results are checked separately.
How FIT1058 is assessed
| Component | Weight | Format |
|---|---|---|
| Quizzes | 10% | Current Moodle controls quiz windows |
| Assignment 1 | 10% | Current Moodle controls deadline and rules |
| Mid-semester test | 15% | Current Moodle controls date and coverage |
| Assignment 2 | 25% | Current Moodle controls deadline and rules |
| Final assessment · hurdle | 40% | Examination-period assessment; 45% component threshold |
Current assessment is quizzes 10%, Assignment 1 10%, mid-semester test 15%, Assignment 2 25% and final assessment 40%. Passing requires at least 45% on the final assessment, at least 45% across in-semester assessment, and at least 50% overall; a failed hurdle produces NH with a maximum unit mark of 45.
Current FIT1058 dates
| Date | Item | Control |
|---|---|---|
| Current S2 teaching period | In-semester assessment | Quizzes, two assignments and mid-semester test total 60%; live Moodle controls dates. |
| Official examination period | Final assessment | 40% with a 45% component threshold. |
Dates are as published in the current course materials. Confirm exact deadlines and submission settings in the live LMS.
What FIT1058 covers
Build the course in three arcs: Sets, Operations and Inclusion-Exclusion establishes the frame, Sequences, Recurrences and Series deepens it, and Graph Theory and Traversal tests the complete method.
Sets, Operations and Inclusion-Exclusion
set · subset · power set · translate collections into set notation and compute operationsDefine set
The course material gives this chapter a concrete anchor: Week 1 directly covers set theory and operations.
- set
- subset
- power set
- Applying set
- Limits of subset and power set
Functions and Relations
function · injective · equivalence relation · test function properties and relation laws from definitionsDefine function
The course material gives this chapter a concrete anchor: Week 2 covers functions, mappings and relations.
- function
- injective
- equivalence relation
- Applying function
- Limits of injective and equivalence relation
Direct, Contrapositive, Contradiction and Induction Proof
direct proof · contrapositive · mathematical induction · select and execute a proof method matched to the claimDefine direct proof
The course material gives this chapter a concrete anchor: Week 3 explicitly covers methods of proof.
- direct proof
- contrapositive
- mathematical induction
- Applying direct proof
- Limits of contrapositive and mathematical induction
Propositional Logic and Normal Forms
proposition · logical equivalence · normal form · build truth tables and simplify propositions with equivalencesDefine proposition
The course material gives this chapter a concrete anchor: Week 4 covers propositional logic.
- proposition
- logical equivalence
- normal form
- Applying proposition
- Limits of logical equivalence and normal form
Predicate Logic and Quantifiers
predicate · universal quantifier · existential quantifier · translate and negate quantified statements preciselyDefine predicate
The course material gives this chapter a concrete anchor: Week 5 extends logic to predicates and quantifiers.
- predicate
- universal quantifier
- existential quantifier
- Applying predicate
- Limits of universal quantifier and existential quantifier
Sequences, Recurrences and Series
sequence · recurrence relation · geometric series · derive terms and sums from explicit indexing and base conditionsDefine sequence
The course material gives this chapter a concrete anchor: Week 6 covers sequences and series.
- sequence
- recurrence relation
- geometric series
- Applying sequence
- Limits of recurrence relation and geometric series
Combinatorial Counting
multiplication principle · permutation · combination · select a counting rule by order, repetition and exclusion structureDefine multiplication principle
The course material gives this chapter a concrete anchor: Week 7 covers counting and combinatorics.
- multiplication principle
- permutation
- combination
- Applying multiplication principle
- Limits of permutation and combination
Number Theory and Modular Arithmetic
divisibility · greatest common divisor · congruence · use Euclidean and congruence reasoning in computing problemsDefine divisibility
The course material gives this chapter a concrete anchor: Week 8 covers number theory.
- divisibility
- greatest common divisor
- congruence
- Applying divisibility
- Limits of greatest common divisor and congruence
Discrete Probability
sample space · conditional probability · independence · calculate conditional and combined probabilities from a declared experimentDefine sample space
The course material gives this chapter a concrete anchor: Weeks 9-10 develop discrete probability in two parts.
- sample space
- conditional probability
- independence
- Applying sample space
- Limits of conditional probability and independence
Graph Theory and Traversal
graph · path · tree · model a network and reason about paths, degree, connectivity and treesDefine graph
The course material gives this chapter a concrete anchor: Weeks 11-12 cover graph theory in two parts.
- graph
- path
- tree
- Applying graph
- Limits of path and tree
It is positioned as a discrete foundations unit for computing.
It treats discrete mathematics as the reasoning language of computing and enforces separate final and in-semester thresholds.
Assessment in fit1058 is distributed as follows: 10% quizzes, 10% Assignment 1, a 15% mid-semester test, 25% Assignment 2 and a 40% final assessment
The operational assessment conditions matter here.
A 40% final assessment is held in the examination period and has a 45% component threshold.
What makes fit1058 demanding is concrete: moving precisely between natural language, symbols and proof while controlling quantifiers, domains, edge cases and the difference between evidence and a valid general argument
Achieve at least 45% on the final assessment, 45% across in-semester assessment and 50% overall; failed hurdles carry NH and a maximum unit mark of 45.
For enrolment planning, Confirm current course-map and prohibition rules in the Handbook.
Build the course in three arcs: Sets, Operations and Inclusion-Exclusion establishes the frame, Sequences, Recurrences and Series deepens it, and Graph Theory and Traversal tests the complete method.
Worked example · free
Disprove a set claim
- 1Declare finite sets and the overlap term.
- 1Recall inclusion-exclusion.
- 1Give A={1,2}, B={2,3}.
- 1Compute union size 3 versus claimed 4.
- 1State the condition under which equality holds.
Key terms
- set
- Well-defined collection of distinct objects considered as a whole. This chapter uses the concept when students translate collections into set notation and compute operations.
- subset
- Set whose every element also belongs to another set. It helps explain the reasoning required to translate collections into set notation and compute operations.
- power set
- Set of all subsets of a given set, including empty set and the set itself. Its limit matters because universe, finiteness and disjointness assumptions determine which counting identity applies.
- function
- Relation assigning each domain element exactly one codomain element. This chapter uses the concept when students test function properties and relation laws from definitions.
- injective
- Function mapping distinct domain inputs to distinct outputs. It helps explain the reasoning required to test function properties and relation laws from definitions.
- equivalence relation
- Relation that is reflexive, symmetric and transitive and therefore partitions a set. Its limit matters because injectivity, surjectivity and equivalence depend on the declared domain and codomain.
- direct proof
- Derivation of a conclusion from assumptions through definitions and established results. This chapter uses the concept when students select and execute a proof method matched to the claim.
- contrapositive
- Logically equivalent implication not-Q implies not-P for P implies Q. It helps explain the reasoning required to select and execute a proof method matched to the claim.
- mathematical induction
- Proof method establishing a base case and an implication from each case to its successor. Its limit matters because checking several cases or restating the conclusion does not prove a universal statement.
- proposition
- Declarative statement assigned a truth value in the logical model. This chapter uses the concept when students build truth tables and simplify propositions with equivalences.
- logical equivalence
- Two expressions sharing the same truth value under every valuation. It helps explain the reasoning required to build truth tables and simplify propositions with equivalences.
- normal form
- Standardised logical expression such as conjunctive or disjunctive normal form. Its limit matters because implication, converse and biconditional have distinct truth conditions.
- predicate
- Open statement whose truth depends on variables from a declared domain. This chapter uses the concept when students translate and negate quantified statements precisely.
FIT1058 FAQ
Where do students usually lose marks in fit1058?
moving precisely between natural language, symbols and proof while controlling quantifiers, domains, edge cases and the difference between evidence and a valid general argument
How is fit1058 assessed?
10% quizzes, 10% Assignment 1, a 15% mid-semester test, 25% Assignment 2 and a 40% final assessment
What is the fit1058 exam or final-task format?
A 40% final assessment is held in the examination period and has a 45% component threshold.
Does fit1058 have a hurdle or component-level pass rule?
Achieve at least 45% on the final assessment, 45% across in-semester assessment and 50% overall; failed hurdles carry NH and a maximum unit mark of 45.
Which offering does this fit1058 guide cover?
It is aligned to Semester 2, 2026; confirm your enrolled class and timetable in the current institutional system.
What prerequisites or restrictions apply to fit1058?
Confirm current course-map and prohibition rules in the Handbook.
Is this fit1058 resource an official university guide?
No. It is an independent fit1058 study resource; current institutional instructions remain authoritative for assessment operation.
Which current fit1058 dates are captured?
In-semester assessment: Current S2 teaching period; Final assessment: Official examination period. Confirm any change and the exact submission setting in the live LMS.
Questions students ask in each FIT1058 chapter
- What is the main task in Sets, Operations and Inclusion-Exclusion?
- Translate collections into set notation and compute operations. Chapter 01 · Sets, Operations and Inclusion-Exclusion
- What is the main task in Functions and Relations?
- Test function properties and relation laws from definitions. Chapter 02 · Functions and Relations
- What is the main task in Direct, Contrapositive, Contradiction and Induction Proof?
- Select and execute a proof method matched to the claim. Chapter 03 · Direct, Contrapositive, Contradiction and Induction Proof
- What is the main task in Propositional Logic and Normal Forms?
- Build truth tables and simplify propositions with equivalences. Chapter 04 · Propositional Logic and Normal Forms
- What is the main task in Predicate Logic and Quantifiers?
- Translate and negate quantified statements precisely. Chapter 05 · Predicate Logic and Quantifiers
- What is the main task in Sequences, Recurrences and Series?
- Derive terms and sums from explicit indexing and base conditions. Chapter 06 · Sequences, Recurrences and Series
- What is the main task in Combinatorial Counting?
- Select a counting rule by order, repetition and exclusion structure. Chapter 07 · Combinatorial Counting
- What is the main task in Number Theory and Modular Arithmetic?
- Use euclidean and congruence reasoning in computing problems. Chapter 08 · Number Theory and Modular Arithmetic
- What is the main task in Discrete Probability?
- Calculate conditional and combined probabilities from a declared experiment. Chapter 09 · Discrete Probability
- What is the main task in Graph Theory and Traversal?
- Model a network and reason about paths, degree, connectivity and trees. Chapter 10 · Graph Theory and Traversal
How to study for the exam
Retrieve the course map, practise the recurring method—declare the universe and notation, translate the claim, choose a definition, proof or counting structure, show each justified step, then test edge cases, negation and a counterexample before interpreting the result for computing—on changed scenarios, and verify every operational assessment detail in the live institutional system.
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