diff --git a/maths/Gaussiandistribution.py b/maths/Gaussiandistribution.py
new file mode 100644
index 000000000000..2ee1516f7ce6
--- /dev/null
+++ b/maths/Gaussiandistribution.py
@@ -0,0 +1,181 @@
+import math
+import matplotlib.pyplot as plt
+from .Generaldistribution import Distribution
+
+class Gaussian(Distribution):
+	""" Gaussian distribution class for calculating and 
+	visualizing a Gaussian distribution.
+	
+	Attributes:
+		mean (float) representing the mean value of the distribution
+		stdev (float) representing the standard deviation of the distribution
+		data_list (list of floats) a list of floats extracted from the data file
+			
+	"""
+	def __init__(self, mu=0, sigma=1):
+		
+		Distribution.__init__(self, mu, sigma)
+	
+		
+	
+	def calculate_mean(self):
+	
+		"""Function to calculate the mean of the data set.
+		
+		Args: 
+			None
+		
+		Returns: 
+			float: mean of the data set
+	
+		"""
+					
+		avg = 1.0 * sum(self.data) / len(self.data)
+		
+		self.mean = avg
+		
+		return self.mean
+
+
+
+	def calculate_stdev(self, sample=True):
+
+		"""Function to calculate the standard deviation of the data set.
+		
+		Args: 
+			sample (bool): whether the data represents a sample or population
+		
+		Returns: 
+			float: standard deviation of the data set
+	
+		"""
+
+		if sample:
+			n = len(self.data) - 1
+		else:
+			n = len(self.data)
+	
+		mean = self.calculate_mean()
+	
+		sigma = 0
+	
+		for d in self.data:
+			sigma += (d - mean) ** 2
+		
+		sigma = math.sqrt(sigma / n)
+	
+		self.stdev = sigma
+		
+		return self.stdev
+		
+		
+		
+	def plot_histogram(self):
+		"""Function to output a histogram of the instance variable data using 
+		matplotlib pyplot library.
+		
+		Args:
+			None
+			
+		Returns:
+			None
+		"""
+		plt.hist(self.data)
+		plt.title('Histogram of Data')
+		plt.xlabel('data')
+		plt.ylabel('count')
+		
+		
+		
+	def pdf(self, x):
+		"""Probability density function calculator for the gaussian distribution.
+		
+		Args:
+			x (float): point for calculating the probability density function
+			
+		
+		Returns:
+			float: probability density function output
+		"""
+		
+		return (1.0 / (self.stdev * math.sqrt(2*math.pi))) * math.exp(-0.5*((x - self.mean) / self.stdev) ** 2)
+		
+
+	def plot_histogram_pdf(self, n_spaces = 50):
+
+		"""Function to plot the normalized histogram of the data and a plot of the 
+		probability density function along the same range
+		
+		Args:
+			n_spaces (int): number of data points 
+		
+		Returns:
+			list: x values for the pdf plot
+			list: y values for the pdf plot
+			
+		"""
+		
+		mu = self.mean
+		sigma = self.stdev
+
+		min_range = min(self.data)
+		max_range = max(self.data)
+		
+		 # calculates the interval between x values
+		interval = 1.0 * (max_range - min_range) / n_spaces
+
+		x = []
+		y = []
+		
+		# calculate the x values to visualize
+		for i in range(n_spaces):
+			tmp = min_range + interval*i
+			x.append(tmp)
+			y.append(self.pdf(tmp))
+
+		# make the plots
+		fig, axes = plt.subplots(2,sharex=True)
+		fig.subplots_adjust(hspace=.5)
+		axes[0].hist(self.data, density=True)
+		axes[0].set_title('Normed Histogram of Data')
+		axes[0].set_ylabel('Density')
+
+		axes[1].plot(x, y)
+		axes[1].set_title('Normal Distribution for \n Sample Mean and Sample Standard Deviation')
+		axes[0].set_ylabel('Density')
+		plt.show()
+
+		return x, y
+		
+	def __add__(self, other):
+		
+		"""Function to add together two Gaussian distributions
+		
+		Args:
+			other (Gaussian): Gaussian instance
+			
+		Returns:
+			Gaussian: Gaussian distribution
+			
+		"""
+		
+		result = Gaussian()
+		result.mean = self.mean + other.mean
+		result.stdev = math.sqrt(self.stdev ** 2 + other.stdev ** 2)
+		
+		return result
+		
+		
+	def __repr__(self):
+	
+		"""Function to output the characteristics of the Gaussian instance
+		
+		Args:
+			None
+		
+		Returns:
+			string: characteristics of the Gaussian
+		
+		"""
+		
+		return "mean {}, standard deviation {}".format(self.mean, self.stdev)
\ No newline at end of file
diff --git a/maths/Generaldistribution.py b/maths/Generaldistribution.py
new file mode 100644
index 000000000000..ae1cf60df508
--- /dev/null
+++ b/maths/Generaldistribution.py
@@ -0,0 +1,41 @@
+class Distribution:
+	
+	def __init__(self, mu=0, sigma=1):
+	
+		""" Generic distribution class for calculating and 
+		visualizing a probability distribution.
+	
+		Attributes:
+			mean (float) representing the mean value of the distribution
+			stdev (float) representing the standard deviation of the distribution
+			data_list (list of floats) a list of floats extracted from the data file
+			"""
+		
+		self.mean = mu
+		self.stdev = sigma
+		self.data = []
+
+
+	def read_data_file(self, file_name):
+	
+		"""Function to read in data from a txt file. The txt file should have
+		one number (float) per line. The numbers are stored in the data attribute.
+				
+		Args:
+			file_name (string): name of a file to read from
+		
+		Returns:
+			None
+		
+		"""
+			
+		with open(file_name) as file:
+			data_list = []
+			line = file.readline()
+			while line:
+				data_list.append(int(line))
+				line = file.readline()
+		file.close()
+	
+		self.data = data_list
+
diff --git a/maths/abs_max.py b/maths/abs_max.py
index e5a8219657ac..4a4b4d9ebca3 100644
--- a/maths/abs_max.py
+++ b/maths/abs_max.py
@@ -7,7 +7,13 @@ def abs_max(x: list[int]) -> int:
     11
     >>> abs_max([3,-10,-2])
     -10
+    >>> abs_max([])
+    Traceback (most recent call last):
+        ...
+    ValueError: abs_max() arg is an empty sequence
     """
+    if len(x) == 0:
+        raise ValueError("abs_max() arg is an empty sequence")
     j = x[0]
     for i in x:
         if abs(i) > abs(j):
@@ -15,13 +21,19 @@ def abs_max(x: list[int]) -> int:
     return j
 
 
-def abs_max_sort(x):
+def abs_max_sort(x: list[int]) -> int:
     """
     >>> abs_max_sort([0,5,1,11])
     11
     >>> abs_max_sort([3,-10,-2])
     -10
+    >>> abs_max_sort([])
+    Traceback (most recent call last):
+        ...
+    ValueError: abs_max_sort() arg is an empty sequence
     """
+    if len(x) == 0:
+        raise ValueError("abs_max_sort() arg is an empty sequence")
     return sorted(x, key=abs)[-1]
 
 
@@ -32,4 +44,7 @@ def main():
 
 
 if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod(verbose=True)
     main()
diff --git a/maths/abs_min.py b/maths/abs_min.py
index eb84de37ce23..00dbcb025cfb 100644
--- a/maths/abs_min.py
+++ b/maths/abs_min.py
@@ -1,13 +1,21 @@
+from __future__ import annotations
+
 from .abs import abs_val
 
 
-def absMin(x):
+def abs_min(x: list[int]) -> int:
     """
-    >>> absMin([0,5,1,11])
+    >>> abs_min([0,5,1,11])
     0
-    >>> absMin([3,-10,-2])
+    >>> abs_min([3,-10,-2])
     -2
+    >>> abs_min([])
+    Traceback (most recent call last):
+        ...
+    ValueError: abs_min() arg is an empty sequence
     """
+    if len(x) == 0:
+        raise ValueError("abs_min() arg is an empty sequence")
     j = x[0]
     for i in x:
         if abs_val(i) < abs_val(j):
@@ -17,8 +25,11 @@ def absMin(x):
 
 def main():
     a = [-3, -1, 2, -11]
-    print(absMin(a))  # = -1
+    print(abs_min(a))  # = -1
 
 
 if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod(verbose=True)
     main()
diff --git a/project_euler/problem_112/sol1.py b/project_euler/problem_112/sol1.py
index d8cb334c9508..b3ea6b35654a 100644
--- a/project_euler/problem_112/sol1.py
+++ b/project_euler/problem_112/sol1.py
@@ -47,7 +47,9 @@ def check_bouncy(n: int) -> bool:
     """
     if not isinstance(n, int):
         raise ValueError("check_bouncy() accepts only integer arguments")
-    return "".join(sorted(str(n))) != str(n) and "".join(sorted(str(n)))[::-1] != str(n)
+    str_n = str(n)
+    sorted_str_n = "".join(sorted(str_n))
+    return sorted_str_n != str_n and sorted_str_n[::-1] != str_n
 
 
 def solution(percent: float = 99) -> int:
diff --git a/project_euler/problem_203/sol1.py b/project_euler/problem_203/sol1.py
index 030cf12f2a85..fe4d14b20c92 100644
--- a/project_euler/problem_203/sol1.py
+++ b/project_euler/problem_203/sol1.py
@@ -75,17 +75,15 @@ def get_primes_squared(max_number: int) -> list[int]:
     >>> get_primes_squared(100)
     [4, 9, 25, 49]
     """
-    max_prime = round(math.sqrt(max_number))
-    non_primes = set()
+    max_prime = math.isqrt(max_number)
+    non_primes = [False] * (max_prime + 1)
     primes = []
     for num in range(2, max_prime + 1):
-        if num in non_primes:
+        if non_primes[num]:
             continue
 
-        counter = 2
-        while num * counter <= max_prime:
-            non_primes.add(num * counter)
-            counter += 1
+        for num_counter in range(num ** 2, max_prime + 1, num):
+            non_primes[num_counter] = True
 
         primes.append(num ** 2)
     return primes