Study block A · reference semester 1
- Calculus
- Linear algebra
← Programme and all study years
Bachelor of Science (BSc) — Mathematics — Academic Support
Year 1
Semesters 1–2 (reference sequence)
Qualification: 3-year bachelor’s route / 4-year honours or research route, where offered. Current purchased LMS term: 12 months. This study section does not sell a new degree or alter an existing learner’s paid expiry.
What is available here: A year-specific reference study map and assignment, plus a shared original foundation workshop with worked reasoning and answered checks. The workshop is supplementary and may recur across related years. The live inventory below identifies existing LMS readings separately. This is not a claim that every textbook, video or semester subject has been completed or reviewed by the degree-awarding university.
Learning outcome and subject plan
Explain and apply calculus and linear algebra, then demonstrate progress through a referenced assignment and a corrected practice portfolio.
Study block B · reference semester 2
- Logic and proof
- Elementary differential equations
Confirm the exact university, award, admission batch, major/minor combination and current syllabus. A fourth-year route is conditional on the university's regulations and eligibility; it is not automatically included in every three-year award.
Original foundation reading and worked example
Mathematics workshop — replace a pattern with a proof
Examples can suggest a proposition but cannot prove a universal statement. Write the domain and quantifiers, identify assumptions, and choose a proof strategy. A counterexample disproves a universal claim even when many earlier examples satisfied it.
Practice situation
Prove that the sum of the first n odd positive integers is n² for every positive integer n.
Worked reasoning
- Check the first cases to understand the statement: 1 = 1² and 1 + 3 = 2². These checks motivate but do not establish the general result.
- Base case: for n = 1 the sum is 1, which equals 1².
- Inductive assumption: suppose 1 + 3 + ... + (2k − 1) = k² for a positive integer k.
- The next sum equals k² + (2k + 1) = (k + 1)². This proves the inductive step, so the claim holds for all positive integers.
- Inspect the proof for circularity: the assumption is made for k, while the conclusion is derived for k+1. State the induction principle rather than merely presenting a sequence of numerical equalities.
Five answered self-checks
Write your answer before opening the explanation.
1. What is the domain?
Positive integers n.
2. What does the base case establish?
The proposition holds at the starting value n=1.
3. What is added in the inductive step?
The next odd integer 2k+1.
4. Why are ten examples insufficient?
They do not cover every positive integer.
5. What would disprove a universal claim?
One valid counterexample within its stated domain.
Your year 1 assignment
Write the proof without looking at the solution, then give a geometric explanation. In later years, compare induction with direct proof and formulate a related sequence whose conjecture fails.
Apply the method to Calculus and compare it with Linear algebra. Submit a source list, one worked application, your first answer, a corrected answer and a short explanation of the correction. For mathematics, keep the chosen topic, data and professional boundaries explicit.
Year-specific focus: Calculus; Linear algebra; Logic and proof; Elementary differential equations. Use your actual prescribed syllabus to choose the relevant paper. A completed foundation workshop alone does not complete these subjects.
Suggested study-session schedule
A repeatable self-study routine, not promised live classes: one session for reading and recall; one for explanation and a worked example; one for independent application; one for correction and cumulative review. Match your university’s semester calendar and available study time. No faculty date, live class or assessed laboratory has been invented.
How the study sessions work
Self-paced reading, tutor-guided explanation and independent practice. These are suggested learning sessions, not a published live faculty timetable. Teacher-led feedback is available only when separately confirmed for your programme.
- Read and recall: Read the selected unit, close the text, and state its main idea and two supporting reasons in your own words.
- Tutor-guided explanation: Ask Course Tutor to explain one specific difficulty and show a worked example. Check citations, calculations and legal/clinical statements against the primary source.
- Apply independently: Attempt a new problem, case analysis, code task or evidence-based essay before opening the model approach.
- Check and correct: Compare your result with the marking criteria. Keep the original answer, correction, reason for the error and one transfer question.
- Review and assess: Revisit the unit in the next study session and at the end of the study block. Combine short recall, application and a cumulative assignment.
Assessment and feedback
Use a short diagnostic, unit practice, a study-block assignment and a cumulative review. Each academic year page includes a worked foundation workshop and answered self-checks; internship sections instead explain institutional requirements. Course Tutor feedback is AI-generated and needs verification; no human marking service is implied.
- Concept accuracy
- 30%
- Reasoning and application
- 30%
- Evidence, sources and method
- 20%
- Clarity and professional presentation
- 10%
- Correction and reflection
- 10%
This is ZELVU’s suggested self-assessment rubric, not the university’s official marking scheme. University examinations, laboratory or field assessment and credit awards remain institutional.
Available protected course reading
16 published reading records in this course; 2 explicitly assigned to this year view. A record count does not establish complete syllabus coverage. Unassigned and legacy resources remain shared course reading.
Assigned year 1 reading
- Calculus: Limits, Differentiation, Integration and Mathematical Modelling
- Linear Algebra: Systems, Vector Spaces, Orthogonality and Eigenvalues
13 shared / legacy reading records — not a complete year syllabus
- Sets, Relations and Functions: The Language of BSc MathematicsStart Here — Learning Roadmap
- Real Numbers: Completeness, Supremum and the Archimedean PropertyCore Learning — Part 1
- Sequences and Infinite Series: Limits and Convergence TestsCore Learning — Part 1
- Groups, Subgroups, Cosets and Lagrange's TheoremCore Learning — Part 1
- Numerical Methods: Root Finding by Bisection, Regula Falsi and Newton–RaphsonCore Learning — Part 2
- Linear Algebra: Vector Spaces, Rank–Nullity and EigenvaluesCore Learning — Part 2
- Ordinary Differential Equations: First-Order Methods and Linear Second-Order EquationsCore Learning — Part 2
- Revision Notes: Limits, Continuity, Differentiability and the Mean Value TheoremsStudy Pack — Revision, Glossary & Practice
- Glossary Builder: Multivariable Calculus — Partial Derivatives, Jacobians and Multiple IntegralsStudy Pack — Revision, Glossary & Practice
- Practice Set: Complex Analysis — Analytic Functions, Cauchy–Riemann Equations and Contour IntegralsStudy Pack — Revision, Glossary & Practice
- Final Revision: Probability, Random Variables and Standard DistributionsStudy Pack — Revision, Glossary & Practice
- Practice Lab 01 — Retrieval, Application & Error AnalysisPractice & Mastery Lab
- Practice Lab 02 — Mixed Assessment & Worked-Solution MethodPractice & Mastery Lab
Source and scope check
This is supplementary academic learning support, not admission to or award of a university degree. The listed sources support duration or reference structure, not endorsement of ZELVU’s material. Institutional paper order, assessment and academic credits remain separate.