GATE DA Conquest Book
Compiled and Signed @ 2026JUL22IST © CC BY-NC-ND 4.0
Conquer GATE DA 2027 by mastering total 10 concepts of this book
available through website, downloadable PDF, or scannable QR code link.
The knowledge of all things is possible.
Leonardo da Vinci
Probability and Statistics: Counting (permutation and combinations), probability axioms, Sam-
ple space, events, independent events, mutually exclusive events, marginal, conditional and joint prob-
ability, Bayes Theorem, conditional expectation and variance, mean, median, mode and standard de-
viation, correlation and covariance, random variables, discrete random variables and probability mass
functions, uniform distribution, Bernoulli distribution, binomial distribution, Continuous random vari-
ables and probability distribution function, uniform, exponential, Poisson, normal, standard normal,
t-distribution, chi-squared distributions, cumulative distribution function, Conditional PDF, Central
limit theorem, confidence interval, z-test, t-test, chi-squared test.
Linear Algebra: Vector space, subspaces, linear dependence and independence of vectors, matri-
ces, projection matrix, orthogonal matrix, idempotent matrix, partition matrix and their properties,
quadratic forms, systems of linear equations and solutions; Gaussian elimination, eigenvalues and eigen-
vectors, determinant, rank, nullity, projections, LU decomposition, singular value decomposition.
Calculus and Optimization: Functions of a single variable, limit, continuity and differentiability,
Taylor series, maxima and minima, optimization involving a single variable.
Programming, Data Structures and Algorithms: Programming in Python, basic data struc-
tures: stacks, queues, linked lists, trees, hash tables; Search algorithms: linear search and binary search;
basic sorting algorithms: selection sort, bubble sort and insertion sort; divide and conquer: mergesort,
quicksort; introduction to graph theory; basic graph algorithms: traversals and shortest path.
Database Management and Warehousing: ER-model, relational model: relational algebra, tuple
calculus, SQL, integrity constraints, normal form, file organization, indexing, data types, data transfor-
mation: normalization, discretization, sampling, compression; data warehouse modelling: schema for
multidimensional data models, concept hierarchies, measures: categorization and computations.
Machine Learning: (i) Supervised Learning: regression and classification problems, simple linear
regression, multiple linear regression, ridge regression, logistic regression, k-nearest neighbour, naive
Bayes classifier, linear discriminant analysis, support vector machine, decision trees, bias-variance trade-
off, multi-layer perceptron, feed-forward neural network; cross-validation: leave-one-out (LOO) cross-
validation, k-folds cross-validation; (ii) Unsupervised Learning: clustering algorithms, k-means/k-medoid,
hierarchical clustering, top-down, bottom-up: single-linkage, multiple-linkage, dimensionality reduction,
principal component analysis.
AI: Search: informed, uninformed, adversarial; logic: propositional, predicate; reasoning under un-
certainty: conditional independence representation, exact inference through variable elimination, ap-
proximate inference through sampling.
PYQs: sample, 2024, 2025, 2026
Appendix: Kindergarten Notebook
Bibliography: My Tastefully Curated Sources of Learning
1 Probability and Statistics
It appears to be a quite general principle
that, whenever there is a randomized way of
doing something, then there is a
nonrandomized way that delivers better
performance but requires more thought.
Edwin Thompson Jaynes
1.1 Counting (Permutation and Combinations)
Counting Ordered Orderless
With Replacement m
n
m+n+1
n
With No Replacement (m)
n
m
n
1. Ordered counting with replacement is an allocation of distinguishable objects with multiplicity
2. Ordered counting without replacement is an allocation of distinguishable objects without multi-
plicity
3. Orderless counting without replacement is an allocation of indistinguishable objects without mul-
tiplicity
4. Orderless counting with replacement is an allocation of indistinguishable objects with multiplicity
1.2 Probability Axioms
Placeholder content for probability axioms.
1.3 Sample Space
Placeholder content for sample space.
1.4 Events
Placeholder content for events.
1.5 Independent Events
Placeholder content for independent events.
1.6 Mutually Exclusive Events
Placeholder content for mutually exclusive events.
1.7 Marginal, Conditional and Joint Probability
Placeholder content for marginal, conditional, and joint probability.
1.8 Bayes Theorem
Placeholder content for Bayes theorem.
1.9 Conditional Expectation and Variance
Placeholder content for conditional expectation and variance.
1
1.10 Mean
Placeholder content for mean.
1.11 Median
Placeholder content for median.
1.12 Mode
Placeholder content for mode.
1.13 Standard Deviation
Placeholder content for standard deviation.
1.14 Correlation
Placeholder content for correlation.
1.15 Covariance
Placeholder content for covariance.
1.16 Random Variables
Placeholder content for random variables.
1.17 Discrete Random Variables and Probability Mass Functions
Placeholder content for discrete random variables and probability mass functions.
1.18 Uniform Distribution
Placeholder content for uniform distribution.
1.19 Bernoulli Distribution
Placeholder content for Bernoulli distribution.
1.20 Binomial Distribution
Placeholder content for binomial distribution.
1.21 Continuous Random Variables and Probability Distribution Function
Placeholder content for continuous random variables and probability distribution function.
1.22 Uniform Distribution (Continuous)
Placeholder content for the continuous uniform distribution.
1.23 Exponential Distribution
Placeholder content for exponential distribution.
1.24 Poisson Distribution
Placeholder content for Poisson distribution.
2
1.25 Normal Distribution
Placeholder content for normal distribution.
1.26 Standard Normal Distribution
Placeholder content for standard normal distribution.
1.27 T-Distribution
Placeholder content for t-distribution.
1.28 Chi-Squared Distribution
Placeholder content for chi-squared distribution.
1.29 Cumulative Distribution Function
Placeholder content for cumulative distribution function.
1.30 Conditional PDF
Placeholder content for conditional PDF.
1.31 Central Limit Theorem
Placeholder content for central limit theorem.
1.32 Confidence Interval
Placeholder content for confidence interval.
1.33 Z-Test
Placeholder content for z-test.
1.34 T-Test
Placeholder content for t-test.
1.35 Chi-Squared Test
Placeholder content for chi-squared test.
3
2 Linear Algebra
Algebra is the offer made by the devil to the
mathematician. The devil says: I will give
you this powerful machine, it will answer
any question you like. All you need to do is
give me your soul: give up geometry and
you will have this marvelous machine.
Michael Francis Atiyah
I can see at least 6 levels of Linear Algebra:
1. Study of matrices and its properties with linear systems solved by elementary methods like substi-
tution, inverse of matrix, and determinant, no vector space is even defined on this level.
2. Study of vector spaces, and how to solve linear systems with intutions of spanning sets of a set of
vectors, no linear map is even defined on this level.
3. Study of linear maps, and how to see linear systems as questions of kernel and image of the linear
map, the transpose is not defined properly on this level, inner product is not defined well either,
all that and dual spaces are made sense through matrices.
4. Study of inner product space, consequently its norm, metric and topology, and even determinant
is defined in terms of linear maps, the dual spaces and dual maps are defined properly giving rise
to a proper definition of transpose.
5. The study of vector spaces over finite fields.
6. The study of infinite vector spaces.
I shall assume all fields F to be infinite, and the dimensionality of all vector spaces over F to be finite,
putting me in the 4th level at most; the syllabus seems to be on 2nd level but I know I shall need ”linear
maps” for optimization, I shall do the study of linear algebra at least at level 3 but since I shall need
inner product spaces, at least Euclidean spaces, for Machine Learning I will penetrate the level 4, though
hardly getting past it, that is I shall avoid getting into dual maps as much as I can.
2.1 Vector Space
I shall be cautious in internalizing vectors, for “vector” itself has no meaning
1
; a vector by definition
is an element of a vector space, and vector space, in turn, should not be internalized in my mind as a
collection of vectors; for a vector inherits its algebra with fellow vectors from the ambiant vector space.
A vector space, then, is a more general and fundamental object constructed out of “set of elements” by
defining two maps, namely the binary operation and the field action; the binary operation on the set
gives me an operation, in this case addition, of the elements of this set, and the field action gives me a
way to scale the elements as I need them to be. As such, a vector space is a set on which addition of
elements is defined along with multiplication of elements of certain set with the elements of the vector
space, which I like to put succinctly as:
Concept 1: Vector Space
A Vector Space
a
on a field
b
is an additive abelian group
c
with a scalar multiplication action
d
by
the same field.
e
a
Also called Linear Space for they are always linear.
b
A set that is both abelian additive group and abelian multiplicative group with a self scalar multiplication action.
c
A set with binary operation · : G × G → G that is associative ·(g
1
, ·(g
2
, g
3
)) = ·(·(g
1
, g
2
), g
3
), has an identity
·(e, g) = ·(g, e) = g, and an inverse for each element ·(g, g
inv
) = e; the uniqueness of identity and inverses is a simple
proof by contradiction.
d
A map F × V → V such that it is additive in scalars (a + b)v = av + bv, additive in vectors c(u + v) = cu + cv,
compatibility of scalar product and scalar action on vectors (ab)v = a(bv), identity action 1v = v, zero action 0v =
0,
and negative unity action (−1)v = −v.
e
This definition of vector space can be made a bit tighter, and is in fact made in standard literature, but this
1
“Arrow” has a completely different meaning, it is an element of “Arrow Space”, that is a vector space on which both
the inner-product and the norm are defined.
4
is both beautiful and eventually the same; that is the action of field elements 0 and −1 on any vector follows from
other assumptions.
Every set based objects have their own maps, which are, as I understand, just functions on their
underlying sets with properties of the functions preserving the structure of those objects; I shall not study
in details, for it’s not in the syllabus, the entirity of linear maps, that is the functions on the underlying
sets of vector spaces that preserve the linear structure, but I shall use its definition:
Concept 2: Linear Maps
A map T : V → W from a vector space to another is linear if i.e., T (c
1
v
1
+ c
2
v
2
) = c
1
T v
1
+ c
2
T v
2
.
2.2 Subspaces
I understand that not any subset is a subspace even if it is set-isomorphic
2
to a subspace; e.g. A line
through origin is a vector subspace of the plane but the same line moved away from the origin is not
3
.
Concept 3: Vector Subspace
A Vector Subspace
a
of a vector space is a subset of the underlying set that is also a vector space.
a
Also called Linear Subspace for they’re always linear.
Incidentally, I see that the verification of a subset of vectors to be a vector space is simpler than that
of the set itself, for the subset inherits several properties from the set; as such it all boils down to the
verification of closedness of the vector addition and scalar multiplicative action on the subset.
4
2.3 Linear Dependence and Independence of Vectors
I want to know if a certain vector belongs to a certain subspace, or if given set of vectors all live in the
same subspace; naturally, I feel the definition as follows:
Concept 4: Linear Dependence
For two vectors, each is linearly dependent with another if one lives in a subspace spanned
a
by
another; generally each vector of a subset of vectors is linearly dependent with others if it lives in
the subspace spanned by the others. Linearly independent if not. Span is always a vector subspace.
a
The span {cv | c ∈ F} of a vector v is the totality of linear multiples cv, c ∈ F. The span {
P
k
i=1
c
i
v
i
| c
i
∈ F} of
a subset {v
i
| 1 ≤ i ≤ k, v
i
∈ V } of vectors is the totality of linear combinations
P
k
i=1
c
i
v
i
, c
i
∈ F.
From which I shall derive the standard definition by noting that if two vectors v
1
and v
2
are linearly
dependent then one lives in another’s spanned vector subspace, which means v
1
∈ span(v
2
) =⇒ v
1
∈
{c
2
v
2
| c
2
∈ F} =⇒ ∃c
2
| v
1
= c
2
v
2
; generally if a subset {v
0
, v
i
}
5
of vectors is linearly dependent then
v
0
lives in the spanned vector subspace of the subset {v
i
| 1 ≤ i ≤ k}, which means v
0
∈ span({v
i
}) =⇒
v
0
∈ {
P
k
i=1
c
i
v
i
| c
i
∈ F} =⇒ ∃c
1
. . . c
k
| v
0
=
P
k
i=1
c
i
v
i
. Now I see the standard definition clearly
that k + 1 vectors are linearly dependent if there exists k + 1 non-zero scalars in the field of the vector
space such that the linear combination
P
k
i=0
c
i
v
i
= 0 is the zero vector. if, however, there exists no such
subset of k + 1 non-zero scalars from the field of the vector space, that is all of them are zero, then the
subset of vectors is linearly independent.
For a finite dimensional vector space V , to which I am constraining my study of the vector spaces,
a subset {v
1
. . . v
n
} of vectors can span the entire space i.e., span({v
1
. . . v
i
}) = V , if, further, the set is
linearly independent, that is there are no redundant vectors in the subset, then the subset is a basis of
the vector space:
2
“Looks similar as sets”.
3
It is an affine subspace.
4
i.e., If ∀v
0
, v
1
∈ S ⊂ V, ∀a ∈ F, v
0
+ av
2
∈ S.
5
v
0
is a generic element, meaning all the following statements are to be true for all elements of the subset of the vectors.
5
Concept 5: Basis and Dimension
A linearly independent subset of vectors spanning the entire space is a basis, and the cardinality of
the basis is the dimension of the vector space.
I see that a linear map T : V (F) → F
n
(F) from an n-dimensional vector space on a field to n-
dimensional vector space F
n
(F) on the same field is an isomorphism
6
for any basis of any finite dimensional
vector space over a field is naturally in bijection with the standard basis of the standard vector space
over the same field, this implies
7
any two finite dimensional vector spaces of the same dimensions are
isomorphic; as such I shall, whenever I may see a need of simplification, use this fact, that:
Concept 6: Finite dimensional vector spaces
Any finite dimensional vector space V (F) on a field F, for a given basis, is isomorphic to the standard
vector space with the standard basis F
n
(F) on the same field.
2.4 Matrices
For a linear map T : V → W from n-dimensional vector space V to m-dimensional vector space W , once I
know where the basis vectors of the domain space V map to in the codomain space W , I know where all the
vectors of V will map to in W ; if a = {v
1
. . . v
n
} is a basis of V , and if {T v
1
. . . T v
n
} are the vectors where
the linear map T maps the basis vectors of V , then for any vector v =
P
n
i
c
i
v
i
∈ V , I know it will map to
T v = T
P
n
i
c
i
v
i
=
P
n
i
T c
i
v
i
=
P
n
i
c
i
T v
i
; if, further, b = {w
1
. . . w
m
} is a basis of W then for any vector
w ∈ W, w =
P
m
j
k
j
w
j
, and in particular T v
j
=
P
m
j
k
j
w
j
; that is T v =
P
n
i
c
i
T v
i
=
P
n
i
c
i
(
P
m
j
k
j
w
j
) =
P
n
i
(c
i
P
m
j
k
j
w
j
) =
P
n
i
(
P
m
j
c
i
k
j
w
j
), if I let f(i, j) := c
i
k
j
w
j
then
P
n
i
(
P
m
j
c
i
k
j
w
j
) =
P
n
i
(
P
m
j
f(i, j)),
and since the sum of all values at each node of a sqaure grid is same if first summed rows or columns,
P
n
i
(
P
m
j
f(i, j)) =
P
m
j
(
P
n
i
f(i, j)) =
P
m
j
(
P
n
i
c
i
k
j
w
j
) =
P
m
j
(k
j
w
j
(
P
n
i
c
i
)) =
P
m
j
(k
j
(
P
n
i
c
i
))w
j
; that
is if T
ab
: V
a
→ V
b
; T
ab
v
a
:= w
b
, is a linear map from a vector space V with basis a to W with basis b
then T
ab
maps v
a
to w
b
.
If I let n = 1 then the domain is a one dimensional vector space which therefore is isomorphic to
F(F); if I let the basis to be standard s, that is s = {e} where e is the identity element of the field, then
by general form T
sb
e
s
:= w
b
∈ W , but e is a scalar from the field, and since T
sb
e
s
has to be a vector,
T
sb
∈ W is a vector, in fact of W , that is T maps e ∈ V in the basis s to T
sb
∈ W in the basis b; from
the general form, since e = 1 · e, T
sb
=
P
m
j
(k
j
(
P
1
i
1))w
j
=
P
m
j
(k
j
(1))w
j
=
P
m
j
k
j
w
j
.
For a given basis b, knowing a vector w of vector space W is equivalent to knowing its “coordinates”,
that is the coefficients of the vector in the given basis; i.e., for the vector T
sb
=
P
m
j
k
j
w
j
in the
basis b = {w
1
· · · w
m
}, w is unambiguously known by the ordered list of coefficients (k
1
, · · · , k
j
) which,
generally in the literature, is written vertically with squared brackets, called column:
"
k
1
.
.
.
k
m
#
; I shall know
that the vectors represented by such columns are called column vectors.
I can see how this might generalize to
Concept 7:
The set M
m×n
(F) of all matrices with entries from a field is a ring
a
; the addition of which comes
from the vector space, and multiplication is the matrix representation of the composition linear
map T
3
: V → U := T
3
= T
2
◦ T
1
where T
1
: V → W and T
2
: W → U
a
A ring is a set with two binary operatinos, an additive and a multiplicative, with standard distributive properties
6
Bijective linear map
7
the converse is also true, that is two isomorphic finite dimensional vector spaces are of the same dimensions.
6
2.5 Projection Matrix
2.6 Orthogonal Matrix
2.7 Idempotent Matrix
2.8 Partition Matrix and Their Properties
2.9 Quadratic Forms
2.10 Systems of Linear Equations and Solutions
I seek the solution set of the system {
P
j
t
ij
v
j
= w
i
| 1 ≤ i ≤ m, 1 ≤ j ≤ n} of m linear equations in
n variables, which in matrix notation is T v = w; I should know they’re called row and colum pictures
respectively
8
, for the latter is a linear combination of vectors, the columns of the system’s matrix, and the
former is a set of algebraic representations of linear manifolds, that is (n − 1)-dimensional hyperplanes,
which can also be seen as an action of a given linear form, that is a row vector, on the column vectors
that form a basis of the vector space.
Either the solution set exists, or it doen’t; I shall know they’re referred to as Consistent, and Incon-
sistent respectively; Either the solution set is singleton, that is the solution is unique, or it isn’t; I shall
know they’re referred to as Definite, and Indefinite respectively; As such I understand that there’re three
possibilities: Inconsistent, Definite-consistent, Indefinite-consistent, for Inconsistent can’t be predicated
with the property of uniqueness.
Concept 8: Linear Systems
Definite-consistent systems, by definition, have only one solution, a point, an affine 0-subspace; In-
consistent systems, by definition, have no solutions, an empty set, and Indefinite-consistent systems,
by deduction, have infinite solutions, affine subspaces; that is non-singleton finite solution set can
not exist
a
.
a
For if T v
0
= 0, so is T (cv
0
) = cT v
0
= 0, ∀c ∈ F, that is if T v
1
= w so is T (v
1
+ cv
0
) = w + cT v
0
= w for all
elements c of the field of the vector space; if the field is infinite, which is what I have assumed for the entire class of
vector spaces I am studying here, then so is the number of general solutions v
1
+ cv
0
.
I wish, now, to decide the consistency and definiteness of linear systems; one fundamental way to
decide the consistency and definiteness of the linear system T v = w is as seeing it as possible linear
combinations of w.
I shall ask if the linear system T v = w, seen as a linear combination T v of the vector w, is consistent,
if it is, I shall ask if it is definite; a linear system w = T v, where T = [t
1
. . . t
n
]
m×n
is an m × n matrix
of column vectors t
i
, is asking if w ∈ span(columns(T )), if it is not, the system is Inconsistent, for no
linear combinations T v =
P
n
i
t
i
v
i
formed by the components of any vector v is capable of building w,
that is w is outside the entire span T has to offer; if, however, w indeed is in the span of columns of T ,
then the system is consistent, for there must exist at least one vector v the components of which makes
the linear combination T v into w.
I shall now ask if a given consistent system is definite; if T v = w is consistent it is saying a certain
set of vectors in the span of T are building up w; I wish to know if there exists only one v, to do so I
shall assume there exists one, but if there exists only one v and since T v is a linear combination building
w, the columns of T has to be linearly independent, for if it they were not I could not have written the
linear combination T v of w uniquely, that is if there exists at least on linearly dependent vector in the
columns(T ) I can scale that vector and still be building w, that is infinite solutions v.
Concept 9: Linear system seen as possible linear combinations
Definite-consistent systems’ matrices are made up of linearly independent columns, the span of
which contains the target vector; Inconsistent systems’ target vectors are not in the span of the
columns; Indefinite-consistent systems’ matrices are made up of linearly dependent columns, the
span of which contains the target vector.
Having decided the consistency and definiteness of a linear system, I shall study a variety of compu-
tational methods, at least the once in the syllabus, of solving linear systems:
8
The latter is a relation on the vector space, while the former on its dual vector space.
7
1. Guassian elimination of linear forms
2. LU decomposition of linear forms
3. Inverse
4. Determinant of column vectors
5. Rank-nullity of linear maps
6. Least Squre
7. Eigenvalues and Eigenvectors
8. SVD
2.11 Gaussian Elimination
2.12 Eigenvalues and Eigenvectors
2.13 Determinant
2.14 Rank, Nullity
Kernel of a linear map is an elegent way to check linear dependence:
Concept 10: Linear dependence in terms of kernel
If kernel
a
of a linear map is trivial then its corresponding matrix is made up of linearly independent
column vectors
b
; linearly independent if non-trivial.
a
Ker(T : V → W ) := {v ∈ V | T v = 0}
b
Since T v is a linear combination
c
P
n
i
v
i
t
i
of the column vectors t
i
by the components of v, if Ker(T ) = {0}
then the column vectors are linearly independent; trivial kernel of a group homomorphism, which a linear map is, is
equivalent to the map being injective, and I see that linear independence is essentially asking if for the kernel of the
map F
n
→ V , assigning linear combinations of a given vector with various coefficients, is trivial.
2.15 Projections
2.16 LU Decomposition
2.17 Singular Value Decomposition
8
3 Calculus and Optimization
Ours, according to Leibnitz, is the best of all
possible worlds, and the laws of nature can
therefore be described in terms of extremal
principles. Thus, arising from corresponding
variational problems, the differential
equations of mechanics have invariance
properties relative to certain groups of
coordinate transformations.
Carl Ludwig Siegel
I shall assume dimensionality of all vector spaces to be finite.
3.1 Functions of a Single Variable
Let f : X → Y be a map between finite dimensional vector spaces X and Y.
3.2 Limit
Placeholder content for limit.
3.3 Continuity
Placeholder content for continuity.
3.4 Differentiability
Placeholder content for differentiability.
3.5 Taylor Series
3.6 Maxima and Minima
3.7 Optimization Involving a Single Variable
9
4 Programming, Data Structures and Algorithms
Science is what we understand well enough
to explain to a computer; art is everything
else.
Donald Ervin Knuth
4.1 Programming in Python
Placeholder content for programming in Python.
4.2 Stacks
4.3 Queues
4.4 Linked Lists
4.5 Trees
4.6 Hash Tables
4.7 Linear Search
4.8 Binary Search
4.9 Selection Sort
4.10 Bubble Sort
4.11 Insertion Sort
4.12 Mergesort
4.13 Quicksort
4.14 Introduction to Graph Theory
Placeholder content for introduction to graph theory.
4.15 Graph Traversals
4.16 Shortest Path
10
5 Database Management and Warehousing
Whether we are based on carbon or on
silicon makes no fundamental difference; we
should each be treated with appropriate
respect.
Arthur C. Clarke
5.1 ER-Model
Placeholder content for ER-model.
5.2 Relational Algebra
5.3 Tuple Calculus
5.4 SQL
5.5 Integrity Constraints
Placeholder content for integrity constraints.
5.6 Normal Form
Placeholder content for normal form.
5.7 File Organization
Placeholder content for file organization.
5.8 Indexing
Placeholder content for indexing.
5.9 Data Types
Placeholder content for data types.
5.10 Normalization
5.11 Discretization
5.12 Sampling
5.13 Compression
5.14 Schema for Multidimensional Data Models
5.15 Concept Hierarchies
5.16 Measures Categorization
Placeholder content for measures categorization.
5.17 Measures Computations
Placeholder content for measures computations.
11
6 Machine Learning
If there is one thing in mathematics that
fascinates me more than anything else (and
doubtless always has), it is neither ‘number’
nor ‘size,’ but always form.
Alexander Grothendieck
6.1 Simple Linear Regression
Placeholder content for simple linear regression.
6.2 Multiple Linear Regression
Placeholder content for multiple linear regression.
6.3 Ridge Regression
Placeholder content for ridge regression.
6.4 Logistic Regression
Placeholder content for logistic regression.
6.5 K-Nearest Neighbour
Placeholder content for k-nearest neighbour.
6.6 Naive Bayes Classifier
Placeholder content for naive Bayes classifier.
6.7 Linear Discriminant Analysis
Placeholder content for linear discriminant analysis.
6.8 Support Vector Machine
Placeholder content for support vector machine.
6.9 Decision Trees
Placeholder content for decision trees.
6.10 Bias-Variance Trade-Off
Placeholder content for bias-variance trade-off.
6.11 Leave-One-Out Cross-Validation
6.12 k-Folds Cross-Validation
6.13 Multi-Layer Perceptron
Placeholder content for multi-layer perceptron.
6.14 Feed-Forward Neural Network
Placeholder content for feed-forward neural network.
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6.15 K-Means/K-Medoid
Placeholder content for k-means/k-medoid.
6.16 Top-Down
6.17 Single-Linkage
6.18 Multiple-Linkage
6.19 Dimensionality Reduction
Placeholder content for dimensionality reduction.
6.20 Principal Component Analysis
Placeholder content for principal component analysis.
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7 AI
This is only a foretaste of what is to come
and only the shadow of what is going to be.
Alan M. Turing
7.1 Informed Search
7.2 Uninformed Search
7.3 Adversarial Search
7.4 Propositional Logic
7.5 Predicate Logic
7.6 Conditional Independence Representation
7.7 Exact Inference through Variable Elimination
7.8 Approximate Inference through Sampling
14
8 PYQs
8.1 Sample Paper
8.2 GATE DA 2024
8.3 GATE DA 2025
8.4 GATE DA 2026
15
My Tastefully Curated Sources of Learning
I cannot remember the books I’ve read any
more than the meals I have eaten; even so,
they have made me.
Ralph Waldo Emerson
Probability and Statistics
[CB24] George Casella and Roger L. Berger. Statistical Inference. CRC Press, Boca Raton, FL, 2nd edition, 2024.
URL: https://www.routledge.com/Statistical-Inference/Casella-Berger/p/book/9781032593036.
[Chu94] Kai Lai Chung. Elementary Probability Theory: With Stochastic Processes and an Introduction to Mathe-
matical Finance. Springer, New York, NY, 4th edition, 1994. URL: https://www.springer.com/gp/book/
9780387948578.
Linear Algebra
[SR13] Igor R. Shafarevich and Alexey O. Remizov. Linear Algebra and Geometry. Springer, Berlin, Heidelberg, 2013.
URL: https://link.springer.com/book/10.1007/978-3-642-30989-2.
Calculus and Optimization
[MN19] Jan R. Magnus and Heinz Neudecker. Matrix Differential Calculus with Applications in Statistics and Econo-
metrics. Wiley, Hoboken, NJ, 3rd edition, 2019. URL: https://www.wiley.com/en-us/Matrix+Differential+
Calculus+with+Applications+in+Statistics+and+Econometrics%2C+3rd+Edition-p-9781119541152.
[Tik86] V. M. Tikhomirov. Stories About Maxima and Minima, volume 1 of Mathematical World. American Mathe-
matical Society, Providence, RI, 1986. URL: https://bookstore.ams.org/mwm-1.
[Tik00] V. M. Tikhomirov. Optimization: Insights and Applications, volume 169 of Translations of Mathematical
Monographs. American Mathematical Society, Providence, RI, 2000. URL: https://bookstore.ams.org/
trans2-169.
Programming, Data Structures and Algorithms
[CLRS09] Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. Introduction to Al-
gorithms. MIT Press, Cambridge, MA, 3rd edition, 2009. URL: https://mitpress.mit.edu/books/
introduction-algorithms-third-edition.
[Lut13] Mark Lutz. Learning Python. O’Reilly Media, Sebastopol, CA, 5th edition, 2013. URL: https://www.oreilly.
com/library/view/learning-python-5th/9781449355722/.
Database Management and Warehousing
[KR13] Ralph Kimball and Margy Ross. The Data Warehouse Toolkit: The Definitive Guide to Dimensional Mod-
eling. Wiley, Indianapolis, IN, 3rd edition, 2013. URL: https://www.wiley.com/en-us/The+Data+Warehouse+
Toolkit%3A+The+Definitive+Guide+to+Dimensional+Modeling%2C+3rd+Edition-p-9781118530801.
[RG03] Raghu Ramakrishnan and Johannes Gehrke. Database Management Systems. McGraw-Hill, New York, NY,
3rd edition, 2003. URL: https://www.amazon.com/Database-Management-Systems-Raghu-Ramakrishnan/dp/
0072465638.
Machine Learning
[GBC16] Ian Goodfellow, Yoshua Bengio, and Aaron Courville. Deep Learning. MIT Press, Cambridge, MA, 2016. URL:
https://www.deeplearningbook.org/.
[HTF09] Trevor Hastie, Robert Tibshirani, and Jerome Friedman. The Elements of Statistical Learning: Data Mining,
Inference, and Prediction. Springer, New York, NY, 2nd edition, 2009. URL: https://hastie.su.domains/
ElemStatLearn/.
GPG fingerprint: 04D9 D396 4A68 998B CBBE 55E9 6D58 7D42 FC82 7E12
[JWHT21] Gareth James, Daniela Witten, Trevor Hastie, and Robert Tibshirani. An Introduction to Statistical Learning:
With Applications in Python. Springer, New York, NY, 2nd edition, 2021. URL: https://www.statlearning.
com/.
[Mur12] Kevin P. Murphy. Machine Learning: A Probabilistic Perspective. MIT Press, Cambridge, MA, 2012. URL:
https://mitpress.mit.edu/books/machine-learning-0.
[Nie15] Michael A. Nielsen. Neural Networks and Deep Learning. Determination Press, 2015. URL: http:
//neuralnetworksanddeeplearning.com/.
AI
[RN20] Stuart Russell and Peter Norvig. Artificial Intelligence: A Modern Approach. Pearson, Harlow, UK,
4th edition, 2020. URL: https://www.pearson.com/store/p/artificial-intelligence-a-modern-approach/
P100000956507.