BCA 107T Mathematical Foundation for Computer Science Notes are a 54-page English study book for BCA Semester 1, batch admitted 2024-25 onwards. They cover all four units, from probability and Bayes theorem to Gauss-Seidel and Simpson's 1/3 rule, with 52 solved numericals, 48 answered two-mark questions and a formula table at the end of every unit.
Written by Prateek Talwar, Founder, Unnati Educations · Reviewed by Ritik Rawat, B.Tech, Senior Full Stack Developer · Checked against the GGSIPU BCA first-year syllabus PDF (syllBCA1styr240124.pdf) · Updated 12 October 2026 · Editorial policy
Scheme: BCA first-year syllabus | Applies to: batch admitted in academic session 2024-25 onwards | Verified against: syllBCA1styr240124.pdf, 12 October 2026
BCA 107T Mathematical Foundation for Computer Science at a glance: GGSIPU BCA Sem 1 credits, units and exam pattern
BCA 107T is the four-credit maths paper of BCA Semester 1, taught over 44 hours. Values come from the official syllabus PDF; anything it does not print is said plainly. It sits with six other theory papers among the GGSIPU BCA Semester 1 papers.
| Paper code | BCA 107T |
|---|---|
| Official title | Mathematical Foundation for Computer Science |
| Course and semester | BCA, first year, Semester I |
| L-T-C | 4-0-4 (4 credits) |
| Paper type | Theory (category code not printed in the syllabus PDF) |
| End-term marks | 60 by the paper-setter pattern (20 + 40 = 60 marks); internal marks not printed in the syllabus PDF |
| End-term exam duration | Not printed in the syllabus PDF |
| Units and hours | Unit I 12 · Unit II 10 · Unit III 10 · Unit IV 12 |
| Question paper pattern | Q1 compulsory: 10 short questions of 2 marks, at least 2 per unit. Then two questions per unit, attempt one, 10 marks each |
| Pre-requisite | Basic Concepts of Mathematics |
| Paired lab | None listed in the scheme |
BCA 107T Mathematical Foundation for Computer Science Notes unit-wise: 52 solved numericals across 4 units
BCA 107T Unit 1: Probability and Probability Distributions
Starts with Kolmogorov's three axioms, proves the addition and multiplication theorems and states total probability. Then come random variables, PMF and PDF, expectation and variance, and the Binomial, Poisson and Normal distributions with a z-table.
Pages 4-20 · 17 sections · 24 solved examples · 12 two-mark answers · 7 ten-mark question types
BCA 107T Unit 2: Interpolation and Solutions of Nonlinear Equations
Also covered as "Interpolation and Nonlinear Equations". Built on the operators E, Δ, ∇ and δ, with six relations between them proved line by line. Difference tables lead into Newton's forward and backward formulae, then divided differences and Lagrange for unequal gaps. Roots come by bisection, false position and Newton-Raphson.
Pages 21-33 · 13 sections · 12 solved examples · 12 two-mark answers · 7 ten-mark question types
BCA 107T Unit 3: Solution of Linear Simultaneous Equations
Writes any system as AX = B and solves it by Gaussian elimination (with a row swap when a pivot turns zero), Doolittle LU decomposition and Gauss-Jordan, which also gives the inverse of a 3 × 3 matrix. Then one system settles in 6 Gauss-Jacobi rounds and 4 Gauss-Seidel rounds.
Pages 34-44 · 10 sections · 7 solved examples · 12 two-mark answers · 6 ten-mark question types
BCA 107T Unit 4: Numerical Differentiation and Numerical Integration
Also covered as "Numerical Differentiation and Integration". Takes derivatives straight from a table, at a tabular point (u = 0) and between values, tested first on y = x³ and then on an eˣ table. Part B covers the trapezoidal and Simpson's 1/3 rules with their error terms, and uses Simpson to reach π ≈ 3.1416.
Pages 45-54 · 9 sections · 9 solved examples · 12 two-mark answers · 6 ten-mark question types
BCA 107T exam corner: 48 two-mark answers and 26 ten-mark question types by unit
The BCA 107T paper opens with ten compulsory two-mark parts, then one ten-mark choice per unit, and each Exam Corner follows that split. No year tags are printed, so treat these as exam-style questions.
| Unit | 2 Marks answered | 10 Marks types listed | Solved numericals |
|---|---|---|---|
| I: Probability and distributions | 12 | 7 | 24 |
| II: Interpolation and nonlinear equations | 12 | 7 | 12 |
| III: Linear simultaneous equations | 12 | 6 | 7 |
| IV: Numerical differentiation and integration | 12 | 6 | 9 |
| Total | 48 | 26 | 52 |
BCA 107T Exam Corner counts by unit, from the notes
- Unit
- I: Probability and distributions
- 2 Marks answered
- 12
- 10 Marks types listed
- 7
- Solved numericals
- 24
- Unit
- II: Interpolation and nonlinear equations
- 2 Marks answered
- 12
- 10 Marks types listed
- 7
- Solved numericals
- 12
- Unit
- III: Linear simultaneous equations
- 2 Marks answered
- 12
- 10 Marks types listed
- 6
- Solved numericals
- 7
- Unit
- IV: Numerical differentiation and integration
- 2 Marks answered
- 12
- 10 Marks types listed
- 6
- Solved numericals
- 9
- Unit
- Total
- 2 Marks answered
- 48
- 10 Marks types listed
- 26
- Solved numericals
- 52
One two-mark question from each unit, with the answer in a line:
- Unit I: State the axiomatic definition of probability. P(A) ≥ 0 for every event, P(S) = 1, and probabilities of mutually exclusive events add (Kolmogorov, 1933).
- Unit II: How many bisection steps give error < 0.001 in (1, 2)? Need 1/2ⁿ < 0.001, so 2ⁿ > 1000. Since 2¹⁰ = 1024, ten steps.
- Unit III: Is x + 10y = 11, 10x + y = 11 ready for Jacobi? No, it is not diagonally dominant. Swap the two equations and it converges to x = y = 1.
- Unit IV: For which polynomials is the trapezoidal rule exact? Degree 0 and 1, because f″(x) = 0 makes its error term vanish.
The BCA 107T notes answer 48 two-mark questions and list 26 ten-mark question types across 4 units, plus 52 solved numericals with step-by-step working.
More practice sits in the BCA 107T important questions.
Bayes theorem in probability: excerpt from page 10 of the BCA 107T notes
Excerpt from page 10
Bayes Theorem
If E1, E2, …, En are mutually exclusive and exhaustive events and A is any event with P(A) > 0, then
P(Ei | A) = P(Ei) · P(A | Ei) / Σj=1..n P(Ej) · P(A | Ej)
Proof
- By conditional probability: P(Ei | A) = P(Ei ∩ A) / P(A).
- By the multiplication theorem: P(Ei ∩ A) = P(Ei) · P(A | Ei).
- By the theorem of total probability: P(A) = Σ P(Ej) · P(A | Ej).
- Putting these in step 1: P(Ei | A) = P(Ei) · P(A | Ei) / Σ P(Ej) · P(A | Ej). Hence proved.
| Term | Name | Meaning |
|---|---|---|
| P(Ei) | Prior probability | Chance of the cause BEFORE we see the result |
| P(A | Ei) | Likelihood | Chance of the result if that cause is true |
| P(Ei | A) | Posterior probability | Updated chance of the cause AFTER seeing the result |
The three terms in Bayes theorem
- Term
- P(Ei)
- Name
- Prior probability
- Meaning
- Chance of the cause BEFORE we see the result
- Term
- P(A | Ei)
- Name
- Likelihood
- Meaning
- Chance of the result if that cause is true
- Term
- P(Ei | A)
- Name
- Posterior probability
- Meaning
- Updated chance of the cause AFTER seeing the result
Applications of Bayes Theorem
- Spam filtering: finding the chance that an email is spam given that it contains words like "free" or "lottery" (Naive Bayes classifier).
- Medical testing: chance that a person really has a disease given a positive test result.
- Quality control: finding which machine most likely produced a defective item.
- Machine learning and AI: Bayesian networks, classification and decision making.
Example 8
In a factory, machines A, B and C produce 25%, 35% and 40% of the total output. Of their output, 5%, 4% and 2% respectively are defective. An item is picked at random and found defective. Find the probability that it was produced by machine A, B and C.
Step 1: Let E1, E2, E3 = item made by A, B, C; D = item is defective.
Step 2: Priors: P(E1) = 0.25, P(E2) = 0.35, P(E3) = 0.40.
Step 3: Likelihoods: P(D | E1) = 0.05, P(D | E2) = 0.04, P(D | E3) = 0.02.
| Machine | Prior P(Ei) | P(D | Ei) | Product | Posterior P(Ei | D) |
|---|---|---|---|---|
| A | 0.25 | 0.05 | 0.0125 | 25/69 ≈ 0.362 |
| B | 0.35 | 0.04 | 0.0140 | 28/69 ≈ 0.406 |
| C | 0.40 | 0.02 | 0.0080 | 16/69 ≈ 0.232 |
| Total | 1.00 | - | P(D) = 0.0345 | 1 |
Example 8 worked in Prior, Likelihood, Product, Posterior form
- Machine
- A
- Prior P(Ei)
- 0.25
- P(D | Ei)
- 0.05
- Product
- 0.0125
- Posterior P(Ei | D)
- 25/69 ≈ 0.362
- Machine
- B
- Prior P(Ei)
- 0.35
- P(D | Ei)
- 0.04
- Product
- 0.0140
- Posterior P(Ei | D)
- 28/69 ≈ 0.406
- Machine
- C
- Prior P(Ei)
- 0.40
- P(D | Ei)
- 0.02
- Product
- 0.0080
- Posterior P(Ei | D)
- 16/69 ≈ 0.232
- Machine
- Total
- Prior P(Ei)
- 1.00
- P(D | Ei)
- -
- Product
- P(D) = 0.0345
- Posterior P(Ei | D)
- 1
Check: 25/69 + 28/69 + 16/69 = 69/69 = 1.
Answer: A: 25/69, B: 28/69, C: 16/69 (machine B is the most likely source).
Do the BCA 107T notes cover the full GGSIPU syllabus?
Yes, for all four units. Every topic the scheme lists, down to "with and without Row Interchange" and the error in each integration formula, has its own section.
One catch: the learning objectives mention Linear Programming, but no unit lists it, so these BCA 107T Mathematical Foundation for Computer Science IPU notes leave it out.
| Unit | Official topics (as printed) | Where in the notes | Status |
|---|---|---|---|
| I | PROBABILITY: Introduction, Axiomatic definition of Probability, Addition Theorem, Multiplication theorem, Conditional Probability, Bayes Theorem and its applications | Sections 1-9, pages 5-11 | Covered |
| I | PROBABILITY DISTRIBUTIONS: Random Variable, Probability Mass function, Probability density function, Mathematical Expectations of a Random Variable, Binomial Distribution, Poisson distribution, Normal Distribution. | Sections 10-17, pages 11-18 | Covered |
| II | INTERPOLATION: Operators: Shift; Forward Difference, Backward Difference Operators and their Inter-relation, Interpolation Formulae-Newton's Forward, Backward and Divided Difference Formulae: Lagrange's Formula | Sections 1-8, pages 22-28 | Covered |
| II | SOLUTIONS OF NONLINEAR EQUATIONS: Bisection Method, False Position Method, Newton – Raphson Method for Solving Equation Involving One Variable only. | Sections 9-13, pages 29-31 | Covered |
| III | SOLUTION OF LINEAR SIMULTANEOUS EQUATIONS: Gaussian Elimination Method with and without Row Interchange: LU Decomposition: Gauss - Jacobi and Gauss-Seidel Method; Gauss – Jordan Method and to find Inverse of a Matrix by this Method. | Sections 1-10, pages 35-43 | Covered |
| IV | NUMERICAL DIFFERENTIATION: First and Second Order Derivatives at Tabular and Non-Tabular Points, | Sections 1-4, pages 46-49 | Covered |
| IV | NUMERICAL INTEGRATION: Trapezoidal Rule, Simpsons 1/3 Rule: Error in Each Formula (without proof.) | Sections 5-9, pages 49-53 | Covered |
BCA 107T official topics mapped to sections and pages of the notes
- Unit
- I
- Official topics (as printed)
- PROBABILITY: Introduction, Axiomatic definition of Probability, Addition Theorem, Multiplication theorem, Conditional Probability, Bayes Theorem and its applications
- Where in the notes
- Sections 1-9, pages 5-11
- Status
- Covered
- Unit
- I
- Official topics (as printed)
- PROBABILITY DISTRIBUTIONS: Random Variable, Probability Mass function, Probability density function, Mathematical Expectations of a Random Variable, Binomial Distribution, Poisson distribution, Normal Distribution.
- Where in the notes
- Sections 10-17, pages 11-18
- Status
- Covered
- Unit
- II
- Official topics (as printed)
- INTERPOLATION: Operators: Shift; Forward Difference, Backward Difference Operators and their Inter-relation, Interpolation Formulae-Newton's Forward, Backward and Divided Difference Formulae: Lagrange's Formula
- Where in the notes
- Sections 1-8, pages 22-28
- Status
- Covered
- Unit
- II
- Official topics (as printed)
- SOLUTIONS OF NONLINEAR EQUATIONS: Bisection Method, False Position Method, Newton – Raphson Method for Solving Equation Involving One Variable only.
- Where in the notes
- Sections 9-13, pages 29-31
- Status
- Covered
- Unit
- III
- Official topics (as printed)
- SOLUTION OF LINEAR SIMULTANEOUS EQUATIONS: Gaussian Elimination Method with and without Row Interchange: LU Decomposition: Gauss - Jacobi and Gauss-Seidel Method; Gauss – Jordan Method and to find Inverse of a Matrix by this Method.
- Where in the notes
- Sections 1-10, pages 35-43
- Status
- Covered
- Unit
- IV
- Official topics (as printed)
- NUMERICAL DIFFERENTIATION: First and Second Order Derivatives at Tabular and Non-Tabular Points,
- Where in the notes
- Sections 1-4, pages 46-49
- Status
- Covered
- Unit
- IV
- Official topics (as printed)
- NUMERICAL INTEGRATION: Trapezoidal Rule, Simpsons 1/3 Rule: Error in Each Formula (without proof.)
- Where in the notes
- Sections 5-9, pages 49-53
- Status
- Covered
Source: official BCA first-year syllabus PDF, applicable from batch admitted 2024-25.
Every course in GGSIPU notes is mapped to its official PDF the same way.
How to write BCA 107T answers: step-wise numericals, iteration tables and two-mark definitions
In BCA 107T the working earns the marks. A ten-mark answer has one shape: definition, formula, short proof, one solved numerical, final answer boxed. Unit by unit:
- Unit 1: lay out every Bayes question as a Prior, Likelihood, Product, Posterior table, and solve "at least one" questions as 1 − P(none).
- Unit 2: forward formula, top diagonal, u = (x − x₀)/h; backward formula, bottom diagonal, u = (x − xₙ)/h. Mixing them is the slip the notes warn about most.
- Unit 3: write each row operation, such as R₃ → R₃ − 7R₂, beside its matrix, then check the answer by substitution.
- Unit 4: check n is even before Simpson's 1/3 rule and tabulate y₀, y₁, … first.
Worked example from Unit 1 (page 7): P(A) = 0.5, P(B) = 0.4, P(A ∩ B) = 0.2. Find P(A ∪ B) and P(neither A nor B).
- State the addition theorem: P(A ∪ B) = P(A) + P(B) − P(A ∩ B).
- Substitute: 0.5 + 0.4 − 0.2 = 0.7.
- Name the link: "neither A nor B" is the complement of "A or B".
- P(neither) = 1 − 0.7 = 0.3. Box both: (i) 0.7 (ii) 0.3.
For two marks, line 1 and the result are enough. For ten, add the proof of the addition theorem from pages 6-7 and a Venn diagram.
Practise this format on GGSIPU BCA important questions.
BCA 107T maths notes FAQs
How do I get the full BCA 107T notes?
Tap "Get Full Notes" at the top or the WhatsApp button at the end of this page. Either one opens a chat with our desk that already carries a BCA 107T reference code. Our team shares the price and payment options in that chat, and once payment goes through, the 54-page PDF covering all four units, with every solved numerical and Exam Corner, reaches you on WhatsApp.
Is there a BCA 107T lab or practical paper?
No. The BCA first-year scheme lists practical papers only for BCA 101P, BCA 103P and BCA 105P in Semester 1, so BCA 107T is a theory paper. Its methods still make good C practice: bisection, Newton-Raphson and Gauss-Seidel are loops that stop when two successive answers agree, which is a short program once BCA 101T loops are clear.
Which BCA 107T unit has the most solved numericals?
Unit 1, Probability and Probability Distributions, with 24 of the 52 solved examples. It runs from dice and card problems through Bayes tables to Binomial, Poisson and Normal numericals with z-table areas. Unit 2 has 12, Unit 4 has 9 and Unit 3 has 7, though the Unit 3 matrix examples take the longest to write out in an exam.
Is Linear Programming part of BCA 107T?
Not in the units. The BCA 107T scheme names Linear Programming in its learning objectives, but none of the four units lists it: they cover probability, interpolation and root-finding, linear simultaneous equations, and numerical differentiation and integration. The notes follow the units, so they do not teach Linear Programming. If your teacher adds it in class, keep a separate operations research text for it.
Do the BCA 107T notes follow the current GGSIPU scheme?
They follow the BCA first-year syllabus applicable to batches admitted from the 2024-25 academic session onwards, and every topic in its four units has a section in the notes. If you were admitted under an earlier scheme, compare your unit list with the syllabus map on this page before buying, because topics or unit order may differ.
What is the passing mark for BCA 107T?
We do not quote pass marks, grace or re-appear rules for BCA 107T, because the university sets them in its ordinances and they can change between batches. Check the current examination ordinance on ipu.ac.in or ask your college exam cell. What the scheme does print is the paper pattern: ten compulsory two-mark parts, then one ten-mark question from each unit.
Get the full BCA 107T Mathematical Foundation for Computer Science Notes on WhatsApp
The full BCA 107T Mathematical Foundation for Computer Science Notes are one 54-page PDF of Mathematical Foundation for Computer Science notes in English: every solved numerical, four Exam Corners and four formula tables.
| Part | Printed pages | Pages | Solved numericals | 2 Marks answered |
|---|---|---|---|---|
| Cover and index | 1-3 | 3 | - | - |
| Unit I | 4-20 | 17 | 24 | 12 |
| Unit II | 21-33 | 13 | 12 | 12 |
| Unit III | 34-44 | 11 | 7 | 12 |
| Unit IV | 45-54 | 10 | 9 | 12 |
| Total | 1-54 | 54 | 52 | 48 |
What is inside the full BCA 107T notes PDF
- Part
- Cover and index
- Printed pages
- 1-3
- Pages
- 3
- Solved numericals
- -
- 2 Marks answered
- -
- Part
- Unit I
- Printed pages
- 4-20
- Pages
- 17
- Solved numericals
- 24
- 2 Marks answered
- 12
- Part
- Unit II
- Printed pages
- 21-33
- Pages
- 13
- Solved numericals
- 12
- 2 Marks answered
- 12
- Part
- Unit III
- Printed pages
- 34-44
- Pages
- 11
- Solved numericals
- 7
- 2 Marks answered
- 12
- Part
- Unit IV
- Printed pages
- 45-54
- Pages
- 10
- Solved numericals
- 9
- 2 Marks answered
- 12
- Part
- Total
- Printed pages
- 1-54
- Pages
- 54
- Solved numericals
- 52
- 2 Marks answered
- 48
Unnati Educations is an independent education provider based in Vikaspuri, Delhi. We are not affiliated with, authorised by, or endorsed by Guru Gobind Singh Indraprastha University (GGSIPU). 'GGSIPU' and 'IPU' are used only to describe the syllabus our notes follow. For official information, visit ipu.ac.in.
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