diff --git a/numerical_methods/babylonian_method.cpp b/numerical_methods/babylonian_method.cpp
index a70fa993e..b08c0d235 100644
--- a/numerical_methods/babylonian_method.cpp
+++ b/numerical_methods/babylonian_method.cpp
@@ -9,9 +9,10 @@
  * @author [Ameya Chawla](https://github.com/ameyachawlaggsipu)
  */
 
-#include <cassert>  /// for assert
-#include <cmath>
-#include <iostream>  /// for IO operations
+#include <cassert>    // for assert
+#include <cmath>      // for NAN
+#include <iostream>   // for operator<<, basic_ostream, cout
+#include <algorithm>  // for max, min
 
 /**
  * @namespace numerical_methods
diff --git a/numerical_methods/bisection_method.cpp b/numerical_methods/bisection_method.cpp
index c93c529d2..c2ef6bfb9 100644
--- a/numerical_methods/bisection_method.cpp
+++ b/numerical_methods/bisection_method.cpp
@@ -13,9 +13,9 @@
  *
  * \see newton_raphson_method.cpp, false_position.cpp, secant_method.cpp
  */
-#include <cmath>
-#include <iostream>
-#include <limits>
+#include <bits/std_abs.h>  // for abs
+#include <cmath>           // for pow
+#include <iostream>        // for basic_ostream, char_traits, operator<<, cout
 
 #define EPSILON \
     1e-6  // std::numeric_limits<double>::epsilon()  ///< system accuracy limit
diff --git a/numerical_methods/brent_method_extrema.cpp b/numerical_methods/brent_method_extrema.cpp
index bd4d2796d..5077f0bd0 100644
--- a/numerical_methods/brent_method_extrema.cpp
+++ b/numerical_methods/brent_method_extrema.cpp
@@ -14,12 +14,14 @@
  * \author [Krishna Vedala](https://github.com/kvedala)
  */
 #define _USE_MATH_DEFINES  ///< required for MS Visual C++
-#include <cassert>
-#include <cmath>
-#include <cstdint>  /// for integral typedefs
-#include <functional>
-#include <iostream>
-#include <limits>
+#include <bits/std_abs.h>  // for abs
+#include <cassert>         // for assert
+#include <cmath>           // for sqrt, cos, pow, M_E, M_PI
+#include <cstdint>         // for uint32_t
+#include <functional>      // for function
+#include <iostream>        // for operator<<, basic_ostream, char_traits, cout
+#include <limits>          // for numeric_limits
+#include <utility>         // for swap
 
 #define EPSILON \
     std::sqrt(  \
diff --git a/numerical_methods/composite_simpson_rule.cpp b/numerical_methods/composite_simpson_rule.cpp
index 2ca58cbe4..14f64bfef 100644
--- a/numerical_methods/composite_simpson_rule.cpp
+++ b/numerical_methods/composite_simpson_rule.cpp
@@ -35,14 +35,14 @@
  *
  */
 
-#include <cassert>  /// for assert
-#include <cmath>    /// for math functions
-#include <cmath>
-#include <cstdint>     /// for integer allocation
-#include <cstdlib>     /// for std::atof
-#include <functional>  /// for std::function
-#include <iostream>    /// for IO operations
-#include <map>         /// for std::map container
+#include <cassert>     // for assert
+#include <cmath>       // for log, sqrt, pow, exp, NAN, isnan
+#include <cstdint>     // for int32_t
+#include <cstdlib>     // for atof, atoi
+#include <functional>  // for function
+#include <iostream>    // for basic_ostream, char_traits, operator<<, cout
+#include <map>         // for map
+#include <utility>     // for pair
 
 /**
  * @namespace numerical_methods
diff --git a/numerical_methods/false_position.cpp b/numerical_methods/false_position.cpp
index ad23d2677..5d83ead34 100644
--- a/numerical_methods/false_position.cpp
+++ b/numerical_methods/false_position.cpp
@@ -22,8 +22,8 @@
  * \author Unknown author
  * \author [Samruddha Patil](https://github.com/sampatil578)
  */
-#include <cmath>     /// for math operations
-#include <iostream>  /// for io operations
+#include <stdint.h>  // for int16_t
+#include <iostream>  // for basic_ostream, char_traits, operator<<, cout, endl
 
 /**
  * @namespace numerical_methods
diff --git a/numerical_methods/golden_search_extrema.cpp b/numerical_methods/golden_search_extrema.cpp
index 2d9dd5070..048679a0d 100644
--- a/numerical_methods/golden_search_extrema.cpp
+++ b/numerical_methods/golden_search_extrema.cpp
@@ -8,12 +8,14 @@
  * \author [Krishna Vedala](https://github.com/kvedala)
  */
 #define _USE_MATH_DEFINES  //< required for MS Visual C++
-#include <cassert>
-#include <cmath>
-#include <cstdint>  /// for integral typedefs
-#include <functional>
-#include <iostream>
-#include <limits>
+#include <bits/std_abs.h>  // for abs
+#include <cassert>         // for assert
+#include <cmath>           // for cos, pow, M_E, M_PI, sqrt
+#include <cstdint>         // for uint32_t
+#include <functional>      // for function
+#include <iostream>        // for operator<<, basic_ostream, char_traits, cout
+#include <limits>          // for numeric_limits
+#include <utility>         // for swap
 
 #define EPSILON 1e-7  ///< solution accuracy limit
 
diff --git a/numerical_methods/gram_schmidt.cpp b/numerical_methods/gram_schmidt.cpp
index c72f8553b..be256cf37 100644
--- a/numerical_methods/gram_schmidt.cpp
+++ b/numerical_methods/gram_schmidt.cpp
@@ -28,12 +28,10 @@
  * @author [Akanksha Gupta](https://github.com/Akanksha-Gupta920)
  */
 
-#include <array>     /// for std::array
-#include <cassert>   /// for assert
-#include <cmath>     /// for fabs
-#include <iostream>  /// for io operations
-
-#include "math.h"
+#include <array>     // for array
+#include <cassert>   // for assert
+#include <cmath>     // for fabs, NAN
+#include <iostream>  // for operator<<, basic_ostream, char_traits, cout
 
 /**
  * @namespace numerical_methods
diff --git a/numerical_methods/midpoint_integral_method.cpp b/numerical_methods/midpoint_integral_method.cpp
index 3eab8fd1e..7a857615d 100644
--- a/numerical_methods/midpoint_integral_method.cpp
+++ b/numerical_methods/midpoint_integral_method.cpp
@@ -18,13 +18,14 @@
  *
  * @author [ggkogkou](https://github.com/ggkogkou)
  */
-#include <cassert>     /// for assert
-#include <cmath>       /// for math functions
-#include <cstdint>     /// for integer allocation
-#include <cstdlib>     /// for std::atof
-#include <functional>  /// for std::function
-#include <iostream>    /// for IO operations
-#include <map>         /// for std::map container
+#include <cassert>     // for assert
+#include <cmath>       // for log, sqrt, pow, exp, NAN, isnan
+#include <cstdint>     // for int32_t
+#include <cstdlib>     // for atof, atoi
+#include <functional>  // for function
+#include <iostream>    // for basic_ostream, char_traits, operator<<, cout
+#include <map>         // for map
+#include <utility>     // for pair
 
 /**
  * @namespace numerical_methods
diff --git a/numerical_methods/newton_raphson_method.cpp b/numerical_methods/newton_raphson_method.cpp
index ce75088a3..7f90cef9e 100644
--- a/numerical_methods/newton_raphson_method.cpp
+++ b/numerical_methods/newton_raphson_method.cpp
@@ -12,11 +12,12 @@
  * \author [Krishna Vedala](https://github.com/kvedala)
  * \see bisection_method.cpp, false_position.cpp
  */
-#include <cmath>
-#include <cstdint>  /// for integral typedefs
-#include <ctime>
-#include <iostream>
-#include <limits>
+#include <bits/std_abs.h>  // for abs
+#include <cmath>           // for pow, NAN
+#include <cstdint>         // for INT16_MAX, int16_t
+#include <ctime>           // for time
+#include <iostream>        // for char_traits, basic_ostream, operator<<
+#include <cstdlib>         // for rand, srand
 
 constexpr double EPSILON = 1e-10;              ///< system accuracy limit
 constexpr int16_t MAX_ITERATIONS = INT16_MAX;  ///< Maximum number of iterations
diff --git a/numerical_methods/ode_forward_euler.cpp b/numerical_methods/ode_forward_euler.cpp
index 5e4dda31b..cc675c5d0 100644
--- a/numerical_methods/ode_forward_euler.cpp
+++ b/numerical_methods/ode_forward_euler.cpp
@@ -36,11 +36,13 @@
  * \see ode_midpoint_euler.cpp, ode_semi_implicit_euler.cpp
  */
 
-#include <cmath>
-#include <ctime>
-#include <fstream>
-#include <iostream>
-#include <valarray>
+#include <cmath>     // for cos, sin, NAN
+#include <ctime>     // for clock, clock_t, CLOCKS_PER_SEC, size_t
+#include <fstream>   // for operator<<, basic_ostream, char_traits, basic_of...
+#include <iostream>  // for cout, cin
+#include <valarray>  // for valarray, __multiplies, operator*, _BinClos
+#include <cstdio>    // for perror
+#include <cstdlib>   // for atof
 
 /**
  * @brief Problem statement for a system with first-order differential
diff --git a/numerical_methods/ode_midpoint_euler.cpp b/numerical_methods/ode_midpoint_euler.cpp
index 50cf4e4c6..1b14a5853 100644
--- a/numerical_methods/ode_midpoint_euler.cpp
+++ b/numerical_methods/ode_midpoint_euler.cpp
@@ -35,11 +35,13 @@
  * \see ode_forward_euler.cpp, ode_semi_implicit_euler.cpp
  */
 
-#include <cmath>
-#include <ctime>
-#include <fstream>
-#include <iostream>
-#include <valarray>
+#include <cmath>     // for cos, sin
+#include <ctime>     // for clock, clock_t, CLOCKS_PER_SEC, size_t
+#include <fstream>   // for operator<<, basic_ostream, char_traits, basic_of...
+#include <iostream>  // for cout, cin
+#include <valarray>  // for valarray, _BinClos, __multiplies, __plus, operator*
+#include <cstdio>    // for perror
+#include <cstdlib>   // for atof
 
 /**
  * @brief Problem statement for a system with first-order differential
diff --git a/numerical_methods/ode_semi_implicit_euler.cpp b/numerical_methods/ode_semi_implicit_euler.cpp
index 01904ac16..b23a81f9f 100644
--- a/numerical_methods/ode_semi_implicit_euler.cpp
+++ b/numerical_methods/ode_semi_implicit_euler.cpp
@@ -35,11 +35,13 @@
  * \see ode_midpoint_euler.cpp, ode_forward_euler.cpp
  */
 
-#include <cmath>
-#include <ctime>
-#include <fstream>
-#include <iostream>
-#include <valarray>
+#include <cmath>     // for cos, sin
+#include <ctime>     // for clock, clock_t, CLOCKS_PER_SEC, size_t
+#include <fstream>   // for operator<<, basic_ostream, char_traits, basic_of...
+#include <iostream>  // for cout, cin
+#include <valarray>  // for valarray, __multiplies, operator*, _BinClos
+#include <cstdio>    // for perror
+#include <cstdlib>   // for atof
 
 /**
  * @brief Problem statement for a system with first-order differential