diff --git a/math/area.cpp b/math/area.cpp
index 691fe91f0..f6ac5f4a8 100644
--- a/math/area.cpp
+++ b/math/area.cpp
@@ -9,11 +9,10 @@
  * @author [Focusucof](https://github.com/Focusucof)
  */
 #define _USE_MATH_DEFINES
-#include <cassert>  /// for assert
-#include <cmath>    /// for M_PI definition and pow()
-#include <cmath>
-#include <cstdint>   /// for uint16_t datatype
-#include <iostream>  /// for IO operations
+#include <cassert>   // for assert
+#include <cmath>     // for NAN, M_PI, pow
+#include <cstdint>   // for uint16_t
+#include <iostream>  // for basic_ostream, operator<<, char_traits, endl, cout
 
 /**
  * @namespace math
diff --git a/math/check_prime.cpp b/math/check_prime.cpp
index ebd48cab5..add436236 100644
--- a/math/check_prime.cpp
+++ b/math/check_prime.cpp
@@ -14,8 +14,9 @@
  * @author [ewd00010](https://github.com/ewd00010)
  */
 
-#include <cassert>   /// for assert
-#include <iostream>  /// for IO operations
+#include <stdint.h>  // for int64_t
+#include <cassert>   // for assert
+#include <iostream>  // for char_traits, basic_ostream, operator<<, cout, endl
 
 /**
  * @brief Mathematical algorithms
diff --git a/math/complex_numbers.cpp b/math/complex_numbers.cpp
index f89238649..0482a088d 100644
--- a/math/complex_numbers.cpp
+++ b/math/complex_numbers.cpp
@@ -7,12 +7,13 @@
  * operators overloaded to accommodate (mathematical) field operations.
  */
 
-#include <cassert>
-#include <cmath>
-#include <complex>
-#include <ctime>
-#include <iostream>
-#include <stdexcept>
+#include <cassert>    // for assert
+#include <cmath>      // for atan2, cos, sin, sqrt
+#include <complex>    // for complex, abs, arg, conj, operator*, operator+
+#include <ctime>      // for time
+#include <iostream>   // for basic_ostream, operator<<, char_traits, cout, endl
+#include <stdexcept>  // for invalid_argument
+#include <cstdlib>    // for rand, srand
 
 /**
  * \brief Class Complex to represent complex numbers as a field.
diff --git a/math/eratosthenes.cpp b/math/eratosthenes.cpp
index 224e9f51b..875fce20b 100644
--- a/math/eratosthenes.cpp
+++ b/math/eratosthenes.cpp
@@ -13,11 +13,13 @@
  * @author [Keval Kapdee](https://github.com/thechubbypanda)
  */
 
-#include <cassert>   /// For assert
-#include <chrono>    /// For timing the sieve
-#include <iostream>  /// For IO operations
-#include <string>    /// For string handling
-#include <vector>    /// For std::vector
+#include <bits/chrono.h>  // for duration, duration_cast, high_resolution_clock
+#include <stdint.h>       // for uint64_t
+#include <cassert>        // for assert
+#include <iostream>       // for basic_ostream, operator<<, cout, endl
+#include <string>         // for char_traits, basic_string, operator==, string
+#include <vector>         // for vector
+#include <ratio>          // for ratio
 
 /**
  * @namespace math
diff --git a/math/extended_euclid_algorithm.cpp b/math/extended_euclid_algorithm.cpp
index cc2eacac8..5fead27b1 100644
--- a/math/extended_euclid_algorithm.cpp
+++ b/math/extended_euclid_algorithm.cpp
@@ -9,9 +9,9 @@
  * multiplicative inverse of a number. (A * B)%M == 1 Here B is the MMI of A for
  * given M, so extendedEuclid (A, M) gives B.
  */
-#include <algorithm>  // for swap function
-#include <iostream>
-#include <cstdint>
+#include <iostream>  // for char_traits, basic_ostream, basic_ostream::opera...
+#include <cstdint>   // for uint32_t, int32_t
+#include <utility>   // for swap
 
 /**
  * function to update the coefficients per iteration
diff --git a/math/factorial.cpp b/math/factorial.cpp
index a6b039da4..f4dffc138 100644
--- a/math/factorial.cpp
+++ b/math/factorial.cpp
@@ -11,9 +11,11 @@
  * @author [Akshay Gupta](https://github.com/Akshay1910)
  */
 
-#include <cassert>   /// for assert
-#include <cstdint>   /// for integral typedefs
-#include <iostream>  /// for I/O operations
+#include <cassert>    // for assert
+#include <cstdint>    // for uint64_t, uint8_t
+#include <iostream>   // for operator<<, basic_ostream, cout
+#include <stdexcept>  // for invalid_argument
+
 /**
  * @namespace
  * @brief Mathematical algorithms
diff --git a/math/fibonacci_fast.cpp b/math/fibonacci_fast.cpp
index 0948276a0..ed33af4eb 100644
--- a/math/fibonacci_fast.cpp
+++ b/math/fibonacci_fast.cpp
@@ -15,9 +15,8 @@
  * @see fibonacci_large.cpp, fibonacci.cpp, string_fibonacci.cpp
  */
 
-#include <cinttypes>
-#include <cstdio>
-#include <iostream>
+#include <cinttypes>  // for uint64_t
+#include <iostream>   // for char_traits, basic_ostream, operator<<, cerr, cout
 
 /**
  * maximum number that can be computed - The result after 93 cannot be stored
diff --git a/math/fibonacci_large.cpp b/math/fibonacci_large.cpp
index e4f4e5eaf..73e696bdd 100644
--- a/math/fibonacci_large.cpp
+++ b/math/fibonacci_large.cpp
@@ -11,11 +11,12 @@
  * @see fibonacci.cpp, fibonacci_fast.cpp, string_fibonacci.cpp
  */
 
-#include <cinttypes>
-#include <ctime>
-#include <iostream>
+#include <stdlib.h>          // for strtoull
+#include <cinttypes>         // for uint64_t
+#include <ctime>             // for clock, clock_t, CLOCKS_PER_SEC, NULL
+#include <iostream>          // for basic_ostream, char_traits, operator<<
 
-#include "./large_number.h"
+#include "./large_number.h"  // for large_number, operator<<, operator==
 
 /** Compute fibonacci numbers using the relation
  * \f[f(n)=f(n-1)+f(n-2)\f]
diff --git a/math/gcd_recursive_euclidean.cpp b/math/gcd_recursive_euclidean.cpp
index 2a3d2183c..368f67cde 100644
--- a/math/gcd_recursive_euclidean.cpp
+++ b/math/gcd_recursive_euclidean.cpp
@@ -6,7 +6,8 @@
  *
  * @see gcd_iterative_euclidean.cpp, gcd_of_n_numbers.cpp
  */
-#include <iostream>
+#include <iostream>   // for basic_ostream, char_traits, operator<<, basic_o...
+#include <stdexcept>  // for domain_error
 
 /**
  * algorithm
diff --git a/math/integral_approximation2.cpp b/math/integral_approximation2.cpp
index eed605e03..b858fedba 100644
--- a/math/integral_approximation2.cpp
+++ b/math/integral_approximation2.cpp
@@ -22,13 +22,14 @@
  */
 
 #define _USE_MATH_DEFINES  /// for M_PI on windows
-#include <cmath>           /// for math functions
-#include <cstdint>         /// for fixed size data types
-#include <ctime>           /// for time to initialize rng
-#include <functional>      /// for function pointers
-#include <iostream>        /// for std::cout
-#include <random>          /// for random number generation
-#include <vector>          /// for std::vector
+#include <cmath>       // for exp, M_PI, sin, sqrt
+#include <cstdint>     // for uint32_t
+#include <ctime>       // for time
+#include <functional>  // for function
+#include <iostream>    // for basic_ostream, char_traits, operator<<, endl
+#include <random>      // for normal_distribution, uniform_real_distribution
+#include <vector>      // for vector
+#include <algorithm>   // for min
 
 /**
  * @namespace math
diff --git a/math/inv_sqrt.cpp b/math/inv_sqrt.cpp
index 1f625e1cf..55088b0c0 100644
--- a/math/inv_sqrt.cpp
+++ b/math/inv_sqrt.cpp
@@ -8,11 +8,12 @@
  * This algorithm is used to calculate shadows in Quake III Arena.
  */
 
-#include <cassert>   /// for assert
-#include <cmath>     /// for `std::sqrt`
-#include <cstdint>   /// for integral typedefs
-#include <iostream>  /// for IO operations
-#include <limits>    /// for numeric_limits
+#include <cassert>      // for assert
+#include <cmath>        // for fabs, sqrt
+#include <cstdint>      // for int32_t, int64_t
+#include <iostream>     // for basic_ostream, char_traits, operator<<, cout
+#include <type_traits>  // for conditional
+
 /**
  * @brief This is the function that calculates the fast inverse square root.
  * The following code is the fast inverse square root implementation from
diff --git a/math/iterative_factorial.cpp b/math/iterative_factorial.cpp
index 12f6afe06..5a3454b28 100644
--- a/math/iterative_factorial.cpp
+++ b/math/iterative_factorial.cpp
@@ -25,10 +25,10 @@
  *
  */
 
-#include <cassert>    /// for assert
-#include <cstdint>    /// for integral types
-#include <exception>  /// for std::invalid_argument
-#include <iostream>   /// for std::cout
+#include <cassert>    // for assert
+#include <cstdint>    // for uint64_t, uint8_t
+#include <iostream>   // for operator<<, basic_ostream, cout
+#include <stdexcept>  // for invalid_argument
 
 /**
  * @namespace
diff --git a/math/large_factorial.cpp b/math/large_factorial.cpp
index 20c677cdc..5f5b5562d 100644
--- a/math/large_factorial.cpp
+++ b/math/large_factorial.cpp
@@ -5,11 +5,12 @@
  * \author [Krishna Vedala](https://github.com/kvedala)
  * @see factorial.cpp
  */
-#include <cstring>
-#include <ctime>
-#include <iostream>
+#include <stdlib.h>          // for atoi
+#include <cstring>           // for strlen, size_t
+#include <ctime>             // for clock, clock_t, CLOCKS_PER_SEC
+#include <iostream>          // for basic_ostream, char_traits, operator<<
 
-#include "./large_number.h"
+#include "./large_number.h"  // for large_number, operator<<
 
 /** Test implementation for 10! Result must be 3628800.
  * @returns True if test pass else False
diff --git a/math/linear_recurrence_matrix.cpp b/math/linear_recurrence_matrix.cpp
index d59ad6aa1..ab5c928d3 100644
--- a/math/linear_recurrence_matrix.cpp
+++ b/math/linear_recurrence_matrix.cpp
@@ -17,10 +17,9 @@
  * here](https://en.wikipedia.org/wiki/Exponentiation_by_squaring).
  * @author [Ashish Daulatabad](https://github.com/AshishYUO)
  */
-#include <cassert>   /// for assert
-#include <cstdint>   /// for integral typedefs
-#include <iostream>  /// for IO operations
-#include <vector>    /// for std::vector STL
+#include <cassert>  // for assert
+#include <cstdint>  // for int64_t, uint32_t, uint64_t
+#include <vector>   // for vector
 
 /**
  * @namespace math
diff --git a/math/modular_inverse_fermat_little_theorem.cpp b/math/modular_inverse_fermat_little_theorem.cpp
index 7550e14bf..bfbd2b419 100644
--- a/math/modular_inverse_fermat_little_theorem.cpp
+++ b/math/modular_inverse_fermat_little_theorem.cpp
@@ -43,8 +43,8 @@
  * (as \f$a\times a^{-1} = 1\f$)
  */
 
-#include <iostream>
-#include <vector>
+#include <stdint.h>  // for int64_t
+#include <iostream>  // for char_traits, basic_ostream, operator<<, cout, endl
 
 /** Recursive function to calculate exponent in \f$O(\log n)\f$ using binary
  * exponent.
diff --git a/math/n_bonacci.cpp b/math/n_bonacci.cpp
index 601b2edf0..066070335 100644
--- a/math/n_bonacci.cpp
+++ b/math/n_bonacci.cpp
@@ -15,10 +15,12 @@
  * @author [Swastika Gupta](https://github.com/Swastyy)
  */
 
-#include <cassert>   /// for assert
-#include <cstdint>   /// for integral typedefs
-#include <iostream>  /// for std::cout
-#include <vector>    /// for std::vector
+#include <cassert>           // for assert
+#include <cstdint>           // for uint64_t
+#include <iostream>          // for char_traits, basic_ostream, operator<<
+#include <vector>            // for vector, operator==
+#include <initializer_list>  // for initializer_list
+
 /**
  * @namespace math
  * @brief Mathematical algorithms
diff --git a/math/ncr_modulo_p.cpp b/math/ncr_modulo_p.cpp
index cbf5e9e1a..f154821c4 100644
--- a/math/ncr_modulo_p.cpp
+++ b/math/ncr_modulo_p.cpp
@@ -9,9 +9,10 @@
  * @author [Kaustubh Damania](https://github.com/KaustubhDamania)
  */
 
-#include <cassert>   /// for assert
-#include <iostream>  /// for std::cout
-#include <vector>    /// for std::vector
+#include <stdint.h>  // for int64_t
+#include <cassert>   // for assert
+#include <iostream>  // for char_traits, basic_ostream, operator<<, basic_os...
+#include <vector>    // for vector
 
 /**
  * @namespace math
diff --git a/math/prime_factorization.cpp b/math/prime_factorization.cpp
index 001c2c3c3..3617ea35c 100644
--- a/math/prime_factorization.cpp
+++ b/math/prime_factorization.cpp
@@ -2,10 +2,10 @@
  * @file
  * @brief Prime factorization of positive integers
  */
-#include <algorithm>
-#include <cstring>
-#include <iostream>
-#include <vector>
+#include <cstring>   // for memset
+#include <iostream>  // for char_traits, basic_ostream, operator<<, basic_os...
+#include <vector>    // for vector
+#include <utility>   // for pair, make_pair
 
 /** Declaring variables for maintaing prime numbers and to check whether a
  * number is prime or not
diff --git a/math/prime_numbers.cpp b/math/prime_numbers.cpp
index cd6aca0ca..50723d9bc 100644
--- a/math/prime_numbers.cpp
+++ b/math/prime_numbers.cpp
@@ -3,8 +3,9 @@
  * @brief Get list of prime numbers
  * @see primes_up_to_billion.cpp sieve_of_eratosthenes.cpp
  */
-#include <iostream>
-#include <vector>
+#include <cstddef>   // for size_t
+#include <iostream>  // for char_traits, basic_ostream, operator<<, cout
+#include <vector>    // for vector
 
 /** Generate an increasingly large number of primes
  * and store in a list
diff --git a/math/primes_up_to_billion.cpp b/math/primes_up_to_billion.cpp
index b7377cea5..d1dc00abf 100644
--- a/math/primes_up_to_billion.cpp
+++ b/math/primes_up_to_billion.cpp
@@ -3,8 +3,9 @@
  * @brief Compute prime numbers upto 1 billion
  * @see prime_numbers.cpp sieve_of_eratosthenes.cpp
  */
-#include <cstring>
-#include <iostream>
+#include <stdint.h>  // for int64_t
+#include <cstring>   // for memset
+#include <iostream>  // for operator<<, basic_ostream, cout, basic_istream, cin
 
 /** array to store the primes */
 char prime[100000000];
diff --git a/math/quadratic_equations_complex_numbers.cpp b/math/quadratic_equations_complex_numbers.cpp
index 3a50719e5..1140e7760 100644
--- a/math/quadratic_equations_complex_numbers.cpp
+++ b/math/quadratic_equations_complex_numbers.cpp
@@ -28,13 +28,13 @@
  * (-0.5,0.866025) (-0.5,0.866025)
  */
 
-#include <array>      /// std::array
-#include <cassert>    /// assert
-#include <cmath>      /// std::sqrt, std::trunc, std::pow
-#include <complex>    /// std::complex
-#include <exception>  /// std::invalid_argument
-#include <iomanip>    /// std::setprecision
-#include <iostream>   /// std::cout
+#include <array>      // for array, operator==
+#include <cassert>    // for assert
+#include <cmath>      // for round, sqrt, pow
+#include <complex>    // for complex, operator==
+#include <cstddef>    // for size_t
+#include <iostream>   // for operator<<, basic_ostream, cout
+#include <stdexcept>  // for invalid_argument
 
 /**
  * @namespace
@@ -65,7 +65,7 @@ std::array<std::complex<long double>, 2> quadraticEquation(long double a,
         solutions[1] = -b * 0.5 / a;
         return solutions;
     }
-    
+
     // Complex root (discriminant < 0)
     // Note that the left term (-b / 2a) is always real. The imaginary part
     // appears when b^2 - 4ac < 0, so sqrt(b^2 - 4ac) has no real roots. So,
diff --git a/math/realtime_stats.cpp b/math/realtime_stats.cpp
index 672acfa03..6a455115d 100644
--- a/math/realtime_stats.cpp
+++ b/math/realtime_stats.cpp
@@ -7,9 +7,10 @@
  * simple enough to be easily implemented in an embedded system.
  * \author [Krishna Vedala](https://github.com/kvedala)
  */
-#include <cassert>
-#include <cmath>
-#include <iostream>
+#include <bits/std_abs.h>  // for abs
+#include <cassert>         // for assert
+#include <cmath>           // for sqrt
+#include <iostream>        // for basic_ostream, char_traits, operator<<, cout
 
 /**
  * \namespace statistics
diff --git a/math/string_fibonacci.cpp b/math/string_fibonacci.cpp
index a7ff4c8bb..34db60e7e 100644
--- a/math/string_fibonacci.cpp
+++ b/math/string_fibonacci.cpp
@@ -8,12 +8,12 @@
  * @see fibonacci_large.cpp, fibonacci_fast.cpp, fibonacci.cpp
  */
 
-#include <cstdint>  /// for integral typedefs
-#include <iostream>
+#include <cstdint>   // for uint64_t
+#include <iostream>  // for char_traits, basic_ostream, operator<<, cout
+#include <string>    // for allocator, basic_string, operator+, string, oper...
 #ifdef _MSC_VER
-#include <string>  // use this for MS Visual C
+#include <string>    // for allocator, basic_string, operator+, string, oper...
 #else
-#include <cstring>  // otherwise
 #endif
 
 /**